Pulled muscle during bench press. Please help

So last week i was doing flat db bench press. I was in a hurry so thought it was ok to skip my warmup set. Big mistake. I pull a muscle not sure what though. Best way to describe it is right underneath my shoulder. So its something in my back. I think what happened was on my descent i went down too far and really streched it outToday (1week later) everything felt fine so i thought id give my chest day another go. I immediately hurt it again.. I have a few questions.
What muscle is this
What is the recovery time
How do i prevent this from occurring again. Was it because I didnt do a warmup set?

I think it may be my Teres Major. Does that sound right?