I'm 4 weeks post op from a partial Supraspinatus tear. This played out over about a year with the original diagnosis as tendinitis. I had a month long course of NSAIDs which did little, then a cortisone injection which relieved the pain, until it wore off 6 months later. Then an MRI which shown the partial tear.
Surgery was scheduled a week later and I'm progressing well. I think surgery was my best option and it sucks not being able to bench or do overhead work for a while, but I'm focusing on lower body and core.
I was told by my ortho that the 1st injection was ok, but subsequent injections would destroy the remaining healthy tendon and make surgery less successful.
Also, be careful lifting on that shoulder after the injection. It will feel great until it wears off and you could do damage until it heals. If it's tendinitis, let it heal up. The injection should reduce the inflammation and slowly help it heal, just don't continue to stress the tendon or you'll end up like me.
Good luck with your healing.