I always pull pronated hook grip and have had this too - usually on my right hand side.
I've had a few right side RC injuries and usually have tightness in this pec, particularly around the attachment site you speak of. I believe the "strain" is from having overly tight pecs. The physio has done deep tissue massage around this area and also has me doing doorway stretches etc, and this seems to have fixed the problem.
So yeah, I'd try address possible pec tightness first.