Answer:

My recommendation would be to stop bench pressing for now. You don't want to make worse what has happened. I would also recommend making a visit to the doctor to get that checked out. You want to be sure you know the cause of it and to be sure you're not doing anything to make it worse.

Be sure you're performing back exercises to offset the chest work.

To work your chest now (if you get doctors clearance), I would suggest doing dips instead. They're just as good, if not better, to be honest. Hold your body in a half-moon position, hunching forward. Set your elbows out wide to the side. That'll give your chest an excellent workout.

If and when you do decide to go back to bench pressing, definitely be sure you're using proper form. It makes a BIG difference.