Don't do push ups (or bench presses) & see a dr.
There are other exercises you can do that'll still maintain chest strength (flies especially, & there are so many variations that you can easily sub them for presses--they can be done w/dumbells, resistance bands, standing, lying, etc.) without straining the shoulder.
Besides, the chest (IMO) is the least important body part where you want to build muscle. The outer pecs are important for, ummm, lift so to speak, but what woman wants that blocky, muscular chest look? You can still give the outer pecs a good workout with a variety of flies until you 1) find out what's wrong w/your shoulder & 2) let it heal.