Hey..I get the same thing when I'm running...but it only occurs a few minutes after I start jogging outside...when I get running and going for a bit, breathing in and out for a while....and then it ceases after about 5-8 minutes of painful jogging.
I do not get this in the gym...
I am thinking that it has something to simply do with the fact that you're breathing in air from outside...in the gym you're breathing in stale gym air...and it's most likely WARMER and thus cold air isn't going into ur lungs? My chest kind of burns when it happens and it happens every time I run outside.
I know many other people who's chests hurt so I don't think it's abnormal. I don't think it's allergies at all...I just think it's maybe for someone who's not in shape? I am in shape with everything but running.