yeah, i usually have a really ****ty eating schedule. like, during the week it wasn't so bad because i could only eat at certain points due to work, and i'd be super hungry so i'd just eat the hell out of whatever i brought, but at home, on the weekends... i'd only eat, like, once a day sometimes ;x i'd just forget. or, on the flipside, i would literally just eat everything ever all day long. both of those regardless of physical activity.
it took me a while to start to figure out "ok, this is actually me being hungry" at, say, work. like, i'd just finished lunch (so, typically, something like a half chicken breast, cup of broccoli cup of kale, handful of mushrooms, about 1/3 a cucumber) and i'd be wanting to eat something else. eventually i figured out i just wanted a little dessert, so i'd grab a bunch of cherry jolly ranchers from a coworkers community pile and just let one slowly melt itself and felt fine.
the lack of eating usually came from when i had a lot of homework to deal with, so i'd just sit down and skip breakfast (not that hungry at that point, usually just due to lack of activity early in the morning) and start working, then next thing i know it's 4 in the afternoon and my gf is asking why i haven't had lunch yet and i have no real good answer because i've even done some pushups to decompress mentally.
though, i guess for you, it should start at the beginning: are you trying to cut down fat? or just maintain a healthy eating habit? if you're trying to cut fat, start tracking your rough caloric intake and keep it around 1900-2100, especially if you're somewhat active. there's a general eyeball measurement for basic needs, i think it's like... if you're really active and male, multiply your bodyweight by.. 18 or 19? that's how many calories you need to just maintain that weight. if you're not really active, it's 14 or 15. i can't remember the article, though. so you can go from there and get a rough idea.
if you want to cut down fat, you eat less than you take in, simple. if you want to maintain you eat close to that amount as possible. if you want to build muscle you'll have to eat over that amount (and it gets complicated the more you want to get lean mass rather than just "bulk up").
and why do you feel awkward doing, say, pushups or squats at home? just asking, that might be something you can work past if you can get down to the root level of it. if you actually find a gym while you're in akita, make sure to work with a trainer who can show you proper form and motions (and help you work on a good beginner strategy). if you can't find someone to help you with that, stick to basic stuff like squat, pushup into benchpress, lat pulls and/or chinups (which are executed slightly differently than pullups). make especially sure to watch squat form, pull up some videos to see how it's done and copy that. so, yes, stick your *** really far out and arch your back in. you don't want to blow something out day 1 and be worthless in all aspects of life for the next month because of that.
old man answered pretty well. walking isn't terrible and it's a start, but remember that walking is essentially controlled falling and we're kind of designed to be able to walk in a low energy manner for extended periods of time. make sure you're trying to walk quickly, you want to be breathing a bit harder and you want to feel your heart moving. even if you have to do that goofy powerwalk stuff, go for it.
i'd say start doing pushups today. just do proper form, and you can just do 5. (proper form means go into an actual plank position, hands right below your shoulders; keep your back straight as your lower yourself down, keep your elbows in closer to your body. control your descent and keep your head up looking forward. when you push back up, don't let your back down. this is going to feel awkward at the start because it engages your core while also using pecs and upper back for the big motion, then using your shoulders to stabilize. just focus on keeping your back straight, make whatever arnold-esque grunting and groaning sounds you have to in order to finish, you got this!)
then do 5 squats.
http://www.bodybuilding.com/exercises/detail/view/name/bodyweight-squat is a good resource for proper form on stuff, btw.
and that can be it. just do 5 of each a day for a week. next week, push yourself to 6 a day. next week 7. so on so on. i was hitting about 100 pushups (5 sets of 20), or 45-ish squats (70 pounds of weight, the most i had at home, 5 sets of 7 or 8), or 45 pullups (5 sets of 9, was working up to 10, but i found out my form was bad, so i actually ended up only doing about 6 or 7) a day before i started working out in the gym and i was not large by any means. so, don't worry about getting really bulky, like i said. you'll have to do A LOT of work to get bulky with just those exercises (and squats will give you ****ing nice thighs and help make your *** look good, anyway : p) and then you'd have to eat to match whatever you're doing in order to gain that bulk.
and the reason i push for strength training stuff to cut off fat is that more muscle mass means you have a higher resting metabolism, which means you burn more calories just sitting around ****posting on swf, which is the highlight of everyone's day here. so, basically, once you hit a point that you're happy with your look (however you want to define this for yourself) you just work on maintaining, so stick to your workout plan and match your calories decently close and you're good.
so i guess tl;dr: cardio is good, but it's good for hearth health which is REALLY important. keep at it. strength training is good for increasing your resting metabolic rate, so do some of that, too. if you want to cut fat, you need a caloric deficit, so increase your resting metabolism and that deficit gets easier to hit.
AND DON'T STARVE YOURSELF. this is really important. go check online what an actual good bodyweight for your height and gender is. if you have the ability, check your body fat percent and try to see how close you are to that. sorry if it comes off as rude, but you'll need to check for the gender you currently are if you haven't started hormone therapy because males and females have different body compositions and metabolisms due to hormones (basically, women have more body fat% in general because fat=baby making fuel. if you're still hormonally male, that matters to a point). make sure that you're checking the information for your activity level as well, because athletes are going to tend to be heavier while having lower body fat% than less active lifestyles.
so, yeah, find out what a good weight for your height is and work out how to get there safely. it's about 3500 calories to make or lose a pound. rda for overall calories is about 2000, so losing a pound in a day (that isn't just waterweight) is really scary. a pound or two a week, especially if you're on the higher end of the range, isn't too bad. but make sure you're eating enough. i'll go kamina you if you're trying to starve yourself down. work on increasing your caloric output, primarily, and try to stick to 2000-2100 a day, low process sugar (so, fruits are cool, candy not so much, and pour that soda down the drain!).
for what you described, an egg is generally about 70-80 cal, and chicken breast... about 230, it looks like from google. lettuce is almost negligible, in terms of calories (like, 5 calories for a cup ;x), so you're really low on calories and i would recommend fixing that. adding other veggies would help, but i'd say if you enjoy cheese, add some to your breakfast, eat another chicken breast at lunch, with some veggies (mix stuff up, too. add in beans and some rice, if you like that stuff. i grew up mexican so i don't like white rice but i ****ing love me some spanish rice!). if you can afford them (and like them) nuts are also pretty good. i personally love almonds and eat the **** out of them, but most any nut is a good deal as long as you watch how much you're eating of them.
if you go too low on calories your body will actually go into starvation mode as a natural reaction and that will slooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooow the **** out of your metabolism. try to hit around 1800-2000, probably, until you get moving up with exercises, then try to hit 2k a day. if you lose bad sugars your metabolism will probably fix a lot of issues on its own, even if you're technically eating more than before.
for swimming you're using a lot of upper body strength. work on upper back and chest/shoulders a lot, since you're essentially using those muscles to literally pull yourself through the water. your legs provide some of the movement and are important overall, but if you want to straight up improve your swim times, strengthen those muscle groups.