OP, You've gotten a lot of good information here.

First step:

As someone what has had multiple upper body injuries from contact sports I strongly suggest you see an orthopedic surgeon specializing in sports injuries. Shoulder injuries do not go away without specific corrective exercises. $200 with a doc and $300-400 for a couple of sessions with a good physical therapist will be the best money you ever spent - the idea is to fix the current issue, and prevent a recurrence.

Second Step:

there are a number of good body-weight calisthenics programs on line, with good tutorials. You don't need to go to a gym, and can incorporate balance exercises as well. A lot of these are sport-specific, and incorporate multiple movements in one exercise. This lets you have a very efficient workout

i play a lot of hockey in the winter (timing is bad for spin classes) and use this - http://247hockeyacademy.com. You can pick and choose, and there are a lot of good upper body and core workouts. You can ignore the hockey-specific bits like stick handling, and structure a really intense 60 minute workout.

TRX is also excellent if you have access to a gym, as is a rowing machine if you learn proper form.

And stretch! If you haven't done a ton of upper body work, learn how to stretch your shoulders and back after a workout