It looks like you have a pretty solid understanding of the fundamentals as far as movement is concerned. You also did well with some feints against the Jiggs where you would act like you're going in, then WD backwards to bait something. That was good. Here is some advice I would like to offer:
1.) Correctly spam more megavitamins. Megavitamin spam in general provides so much utility in this matchup it is unreal and extremely underrated. I have talked with quite a few high level Jiggs players and they agree that Doc. is one of the character's worst matchups because of pills. I say correctly spam them though, because you can use pills in such a way to create more options for Doc.
2.) Use more nairs. SH nairs and full-hop nairs are great, especially against a character like Jiggs that will die at low percentage. A lot of players don't expect the nair to become stronger as it's out. It is also a great spacing move when going through the opponent's shield.
3.) Do not DI in when you get hit by a bair or fair off stage. DI away on the first bair. It may seem like a bad idea at first, but it increases the probability of recovering. If you keep DIing in, you will feel the Jiggs Wall of Pain and lose a stock in the process.
4.) Do not be on a platform above Jiggs. It is just never a good idea unless an option presents itself during a combo or something similar to that kind of situation.
5.) Use more full-hop dairs. Full-hop dairs are very useful, especially against floaties. It does a lot of damage and the priority on dair is very strong.
6.) Use more WD back to fsmash, ftilt baits. This works very well against characters that use aggro with a forward momentup toward you as an approach (fox, falco, CF, Jiggs). A great way to punish and rack up damage.
7.) Use doc's up+B to beat other hitboxes while recovering so you can land on the stage safely. Even if you trade, the hit-stun and trajectory the opponent experiences will buy you enough time to safely recover. Most of the time it should not trade though because the up+B hitbox has very high priority.
In response do your question regarding Doc. vs. Sheik and the matchup, it is one of Doc's toughest matchups. It is definitely possible to beat her, but it is quite difficult. Also, Doc. does well vs. Spacies but it really only shines if you know the matchup better than they do. Doc. on FD vs. basically anyone is usually the best idea. If you ever decide to use Doc. against someone and they ban FD, it might not be a bad idea to assume they have some decent Doc. matchup experience.
I'm sure there is more I could discuss. Hope this helps though.