Cobalt's right
If you do shoulder girdle strengthening exercises, push ups should be OK. Just don't squeeze your shoulder blades together when you're doing push ups. Keep your shoulder set and don't move them. The only thing that should be moving in a push up is your elbow.
Please don't do them if it hurts your shoulders.
And I would be remiss if I did not congratulate you on getting to where you're at right now!