Are you a football player?? 6'4 - 350lb....Is the 350 lbs all muscle??
It might have to do with your weight and also eating unhealthy might exacerbate the situation. If i were you i would cut back on the junk food and sugary products. Also, getting to a healthy weight/height ratio would be ideal. At, 6'4 you should try to be around 220 - 260 solid muscle. IMO, at 6'4 you are physically threating to the majority of males so there's no point in carrying extra weight. (unless you're a football player and you need the weight for your position)
Start doing some long distance walking to increase blood flow and aerobic endurance. After, you feel comfortable with the long distance walking, beginning to run, weight train, etc. (start slow and then increase) Start eating healthy foods, Whole grains, whole wheat breads etc. Buy a multi-vitamin.
Cut back on sodas, junk foods, fried foods,etc.
I would see a gi doctor.
RCasey, I know it has been a while since you wrote this entry, but I did want to say it sounds like one of two things that my family has had to deal with extensively. One is a hiatal hernia (I need to look up spelling again, sorry, heh) in the upper GI tract. It can cause the exact symptoms you are having. The other is deferred pain form arthritis of the spine, but that was from someone in their fourties, so not sure it would apply to you.
Seriously, the hiatal hernia can be devastating and cause so much pain. Mine made me think I was having a heart attack on several occasions until I got the diagnosis. It is not immediately life threatening, but it can possibly lead to esophagial cancer if not treated long term. There is a way of successfuly treating it but it takes experimentation. I hope you have found relief, but if not look into this. Good luck