I don't want to scare the shit out of you, so keep in mind that this most likely has NOTHING to do with what you're experiencing:
As I said, I've had a similar experience. The bench press was the only lift I really felt it in and while it was pretty bad during the light lifts it almost didn't hurt on the big ones.
Months passed and at one point (actually two) I talked with my doctor about it. He, like I, assumed that it was just a matter of my tendons/ligaments struggling to keep up with my increase in strength and muscle mass (was going pretty fast in the beginning).
Then one day I woke up to find that my right shoulder (the painful one) was completely fucked to the degree where I could barely lift a big glass of water out in front of me.
Doctor -> specialist/ultrasound -> physiotherapist led to the conclusion that I'd suffered a luxation of my shoulder and that my AC joint was pretty messed up - swollen and gaping. My physiotherapist insists that it must be the product of a sudden trauma to the shoulder when doing martial arts, but I remember no such thing and was actually taking the week off from training when I woke up with the injury.
I'm now in the latter part of rehab (ended up getting a steroid injection) and as the weights are going up in the BP, the pain is starting to return. I don't quite know what to make of it.
I'm still not convinced that this didn't have something to do with the pain I'd been having many months before in that exact shoulder, in that exact place.
I guess what I'm saying is that you shouldn't take it too lightly and that you might won't to get it checked out or something if it doesn't go away.