Does it feel tight during your the concentric phase of the lift?
Do you bench in a shirt or are you raw?
If I were you I would try and find a massage therapist in the area who specializes in athletes because they will be able to loosen up the muscles and hopefully prevent you from tearing your pec or a tendon.
Also you can definitely back off for a week and just work your upper end by doing higher boards. If you are benching correctly then you should really notice the issue if you stay around a 3 and 4 board press. If you're a raw bencher then try using a 1 board or a half foam roller on your chest while benching and don't go crazy with your numbers, just maybe work up to your opener and stick with singles. Remember you aren't going to build any noticeable strength in the next few weeks but you can easily set yourself really far back.
Personally what I do now is before every bench session I use a lacrosse ball to roll out my chest and a trigger wheel to roll out my biceps. I also apply some lineament to help loosen things up and I really exaggerate my warm up to make sure everything is loose. Finally I do some general stretching nightly to keep the area loose and make sure I have the adequate ROM needed to bench safely.