The main problem is that after the injection your shouder feels better, so you use it more actively, damage it more, and eventually it gets worse. The injections can be very good, but you must not stress the joint afterwards.
It is probably wiser to see if you can manage using a normal painkiller....paracetamol or the like.
Cortisone injections can promote crystalline deposits in the joint(s), leading to arthritis & rheumatism in later life.