Butt winking, especially if you can squat fairly deep, is typically a motor control issue. Your breathing and bracing strategy my not be ideal and you may be trying to squat deeper than you need to with weight. Look back at the episodes Kaitlin suggested and take a look at your stance and depth. The human body, at the very end ranges of a squat, is meant to have a butt wink for pooping. If you are squatting with a bar (front, back, overhead, etc) you only need to break parallel so don’t chase depth you don’t have control over.

Alex

This is likely a set up and technique related issue. These kinds of issues tend to happen in people who pull with a flexed spine and then fixate the bar overhead while they back is in over extension. There can be a lot that leads to this but start with making sure you understand how to brace your spine from the beginning and keep it in a good position the whole time. This probably means going back to squats and overhead squats and looking at how you do them. Then you can go see whats happening at the shoulders and upper back and hips and ankles. The snatch requires a tremendous amount of skill, mobility, and motor control. Many people do them because that is what the gym says to do when they should really be modifying the movement.

Continue with what you are doing, especially the things that you are finding helpful. You also need to look at your training and find things that you can do that you can progressively overload that don’t aggravate the situation. You have to figure out what you can do and work there as hard as you can and let your body reduce the sensitivity to the situation. Some of the big ones for this are any of the trunk work on the site, use as light a ball as you need, and making sure you get movement into the hips without aggravating your back. Thinks like deep goblet squats and sled work can be great here. 

Don’t worry about getting more dorsiflexion. Given the mechanism of the problem, you likely aren’t going to gain much. It is best to do your squatting with load to a box that allows you to keep your heels down (even if it is above parallel, doesn’t really matter anyway) and load up things like deadlifts and heavy carries and sled work to improve leg strength, even subbing split squats is a good alternative. Don’t get caught up thinking you have to squat below parallel with a bar on your back to achieve your personal fitness goals.

Avoid the injections. See someone who understands training and also has a certification in KBs and can teach you real arm bars and turkish get ups and presses. There is likely some reworking of how you are using your shoulder that is not being addressed that you could spend time on and work it out. Particularly learning to use your lats and teres major and create better rotator cuff activity through grip, traction and compression (farmers carries and the arm bars, get ups, crawls, etc..)

While an injection may cause a decrease in the pain symptoms (no guarantees) it doesn’t really solve any of the problems that are leading to you inflaming your bursa. Make sure you have a plan to correct whatever issue is causing the problem.