I'm a recovering addict and I tore a rotator cuff and caused some pretty gnarly nerve damage in my left shoulder/upper arm after overdosing on heroin, fentanyl and benzos three years ago. I have almost all feeling back now other than a few spots where all sensation is very dulled down, it will most likely always feel that way. The cuff has since healed and I have full mobility again, before I could hardly lift my arm. For the longest time really fucked my skating and fucked my skiing even more (I do a lot of inverts, switch ups on rails, etc. where you absolutely need every muscle in your body). My rotator cuff does get sore far easier than it used to however. Not sure if it's due to the surrounding nerve damage or due to the actual healed tear. I did start my physical therapy exercises far later than I should have because I was still using and depressed at the time (2.5 years clean though!)
The main things that helped me were physical therapy, yoga, and lifting weights. I kept the weight low but the reps high. I'd recommend looking at different physical therapy exercises for your specific injury, doing some basic yoga and stretching, and if your injury allows you to safely life weights you can give that a go as well.
NSAIDs like Ibuprofen, Naproxen, Diclofenac, and so forth will help with inflammation and pain management. Be careful though as they are hard on your stomach and liver. CBD works very well too but I find NSAIDs to work MUCH better but have far more negative side effects. Avoid opioids like the plague... if you're like me you'll go from swallowing a 10mg Oxycodone injecting hella bags of heroin in a Kwik Trip bathroom. I'm on Suboxone (buprenorphine) currently and it did/does help with the pain but honestly I found the NSAIDs to help more. Not worth fucking with opioids.
Take it slow, be consistent, and stay positive. Eating healthy always helps as well.