My background is in Athletic Training, so almost all of my experience with injuries are with athletes who usually (although not always) have athletic injuries.
Your toeing a dangerous line when pushing through pain. In the course of returning from an injury I typically advise people that if it hurts that means it's too much too soon. Your average musculoskeletal injury like a strain or a sprain will feel 100% before it is actually healed 100% and capabale of taking the same pre-injury stress. While pain typically means to some extent reinjury, there are occasions when it is appropriate to push through a little discomfort, but if you have to ask then you probably should ease off when you feel pain.
That said, pain and hurt means different things to different people, different injuries and diseases all feel different and have different intensities and characteristics. I've seen a kid who cut his thumb off with a table saw beg a doctor NOT to give him a novacaine injection because the injection hurt worse than losing his thumb.
The only advice I can give you is to go see someone who can tell you if it is safe or a good idea to push through it, that's not something anyone can tell you over the internet.
Oh, if you're talking about chest pain as described here
http://www.americanheart.org/present...dentifier=4472 then you need to stop the activity immediately and see a doctor ASAP.