Im not a doctor or anything but some people in my family has had that feeling and its either stress which makes it where he can have a heart attach if he dosent take it easy.. he needs to go to the doctor... they can tell him and help him out with whatever it might be.. good luck.
It is known as 'soldiers heart' (Da costa syndrome). Not a serious problem but do get checked to be sure.
At first this sounded like a heart attack...how old is your boyfriend? Is he having an irregular heartbeat or anything? I would call the hospital and talk to somewhere there, or head straight to the hospital and get him checked out. It may not be a full-blown heart attack, just an angina, and the sooner you get to the hospital the better. Don't freak out but just get it checked out. If he feels dizzy, gets breathless, sweaty or his heart beat gets fast or "fluttery" you should go to the hospital. The best thing that can happen is it's a false alarm