Should I stop doing push ups and chest exercises after my breast implants?

This is highly dependent on what your surgeon did exactly, how the surgery "went" and even what type of implants you have.When I use smooth implants submuscular in female bodybuilders/fitness competitors, if the surgery and early recovery are totally normal, I allow them to resume whatever activities - strenuous or not- they choose after one week. This has not caused any issues. BUT.....clearly just because they are allowed does NOT necessarily mean they are comfortable. Most ease into it with some cardio, light arms them maybe some abs/legs. Chest and back tend to be the last but they let their body guide them.YOUR surgeon is the only one whose advice you should follow on this.

 As a general rule of thumb is safe to walk at a slow pace immediately after surgery, to do light cardio at around two weeks, and to begin working your upper body at 6 weeks. That said, it is critical that you check with your surgeon, since details of your particular surgery can have a huge impact on this timeline.Textured or anatomical shaped implants, excess bleeding at the time of surgery, and the rate of healing can all be reasons to wait closer to 8-12 weeks for heavy lifting. 

Check with your surgeon to find out his or her protocol for returning to the gym. I tell my patients they can return to their chest presses, dumbbell flys and push-ups easily from the 5th or 6th week on. It's just important to listen to your body; if you feel sore, you should take it easy. I have Triple Crown bodybuilders who went back into competition after getting implants. They started with light training at six weeks and heavier training after eight weeks. For more information on this and
similar topics, I recommend a plastic surgery Q&A book like "The Scoop
On Breasts: A Plastic Surgeon Busts the Myths."