If you're chest pain goes away when exercising and you're 25 years old it's caused by stress. The burning sensation is weird, stabbing or localized pains are common, not a burning sensation. Do you have acid reflux as well?
Finish the PhD quickly and open a fish farm in Oregon, find a pretty (low maintenance) wife, don't go into debt, hike every day, stop eating chillies and drinking beer, and live a simple stress free life.
I would venture that you're stress sensitive, and if you go into a major career it will only get worse until eventually in approximately 20 years you will die from coronary heart disease. I've seen it happen twice this year to men in their early 40s working in high stress jobs in my own profession, and now it seems to be happening to me.
This post may sound flippant, but it is meant to be deadly serious. You have to decide what you value most in life, health or wealth.
Sounds like heart burn, but I would check it out