Sorry to hear about your shoulder. I'm not sure what type of tear you had but I had a traumatic brachial plexus traction injury a when I was 21. It took about 5 months before I had any motion in the arm (though I could move my fingers by the end of the first month -just no coordination), had almost no motion and then one night the arm just shot out across the bed-starling but after that I was actually able to begin moving it a bit. As the nerve healed it went through periods of being very uncomfortable with a lot of tingling but there were also times when it would calm down. 4 years of intensive physical therapy (4x a week minimum) at a top hospital and I'm in pretty good shape now, still don't have full ROM but can do most of what I need to do. Headaches were an unfortunate side effect for a long time, but have gotten much better. Right now I'm working on retraining the muscles to learn how to throw a ball and some other gross motor skills. When it first happened I was told I should be on high doses of painkillers and take a semester off school but I turned both of those things down and ended up completing the semester with great marks. I think one of the biggest things with this type of injury is that it's part of your life for quite a while, but the frustration becomes less and less frequent and if you commit yourself to physical therapy and know where you want to go, you can recover. It just takes a very long time.
Anyway, when I went to disney the biggest things were keeping it supported (not hanging down) and iceing it a lot. There were a few embarrasing moments getting in and out of vehicles -simply because I didn't have great use of the arm at the time- but nothing noticable and all of them could have been avoided if I had just accepted that I had to do things slightly differently (like taking my time getting into/out of vehicles). If you can have a good sense of humor about it-even when it is driving you crazy-that really helped me.
The key I found was to stay ahead of the pain/discomfort as much as possible. The things that I found helped the most were: 1. to get one of those drawstring backpacks with super thin straps (didn't put too much pressure on the arm/shoulder or neck); 2. packing extremely light, bringing icepacks (the throw away kind that you just shake to use -buy these in florida if you're flying because they can cause issues at the airport security wise) though you can get them in the guest/first aid centers, I typically didn't want to go out of my way to find one of those and explain the situation to them so carrying them in my backpack meant that I was more likley to use them -when I was at the hotel they were great about providing me with icepacks so I would recommend calling the front desk to ask-if your staying somewhere with a freezer in the room, you can just use a few reusable ones; 3. wearing an underarmor (tight) sport tanktop that did not put pressure on my shoulder but that I could stick the icepack under so I wasn't forced to hold it -especially on the rides (it took a while to find a tank top that didn't cause my arm to tingle but was tight enough to hold the icepack in place); 4. take ibprofen or tylenol to stay ahead of the pain and ice at night before you go to bed and in the morning before you go to the parks (plus while you are at the parks.); 5. if the handicap restrooms are available use them (if you haven't already noticed this, it will become very apparent when you get to disney-when the toilet paper is on the side with the bad arm in some of the cramped little normal stalls, it can be difficult/annoying to reach over with your good arm to grab it without twisting awkwardly); 6. wear athletic shorts or something without a button, unless you are very dexterious with your left hand, when you are trying to get in and out of the bathroom with a billion other people, you don't want to spend the extra time trying to button your shorts with one hand; 7. if you are going to go on rides that jostle you around be VERY careful, if your arm gets jammed into something or someone you may end up feeling it the rest of your trip. If you are adament about going on those type of rides try to go at the end of the day so you can go back to the hotel and ice right after and try to get someone in your party who is strong enough to brace themselves to sit on the side where your arm is hurt so that they don't slam into you during the ride and can prevent you from smashing into the side of the ride with your bad arm; 8. if you go on slower rides or shows where the seats have an armrest, try to get an end of the row seat or sit with someone you trust on the side where your arm is injured so you can rest it on the armrest -without worring about the person next to you leaning on you or taking up the armrest- if you're in a sling your neck will really thank you for taking the stress off it for a little bit; 9. take advantage of the pool if your hotel has one -even if it means going in the evening after any of the kids are asleep, taking the pressure off your arm and neck in the water can really help to avoid muscle stiffness and more pain. 10. have whoever you are with do an ice massage (take some icecubes and one by one and have a friend take them 1 by 1 and just gently place/rub them over the whole shoulder area-it feels wierd but does help in the long run) before bed every night. I think those are the biggest things I remember from my trip...
In terms of the antibiotics/shade, I have been in the parks on medication that makes me suceptible to sunburn and I never felt the need to use a GAC My mother has an illness where she is basically allergic to the sun so needs to avoid it and she never used a GAC either. Both of us wore baseball hats and lots of sunscreen. Disney was built with a lot of though put into the sun factor. Many of the rides have shaded lines and there are a lot of options that are inside. We simply planned to do the rides in direct sun in the morning, late afternoon, and evening, switching off between a "sun ride" and then two "shade rides." At MK the TTA and the Carosel of Progress are great "break from the sun" rides that are somewhat slow moving and give you a good break from the sun. In Epcot the rides at the Land and Spaceship Earth are good out of the sun options. We were actually both suprised at how much being in the sun was NOT an issue for us. We also stayed on property the first two times and went back to the polynesian from like 1-3 everyday to swim (kids) and rest (most of the adults-except whoever was on pool duty).
That may be more info than you needed, but I hope it helps. It definitely is a frustrating injury, but it does get better. If you have any other questions, feel free to ask! Good luck!