Some of us are affected by changes in barometric pressure. I am, quite severely, and can predict a storm HOURS before the weather morons. It presents with pressure in my head and sinuses and I'm often convinced I'm about to get a migraine because my vision is slightly distorted. I have been told by my neuro that that is caused by the intense sinus pressure pushing on my optic nerve.
It could, in my humble opinion, be a manifestation of anxiety. (Do thunder storms make you anxious?)
The tightness in your chest is classic for anxiety............I think you would benifit from learning some breathing exercises to help relax the diaphram and also to prevent yourself from hyperventilating.
The frequent burping and the feeling of needing to throw up can also be part of anxiety, but personally I think you should check the expiration date on that buffalo you ate.
You asked if this could just be part of the anxiety, but you don't say if you have an anxiety disorder or if you're on any meds. It's possible this was simply a transient bout of anxiety due to the storm or having a dead buffalo in your house, and you will have no further problems. But, I will say that if these feelings don't go away, get worse or you begin to experience them more frequently, a visit to your doctor is definitely called for.
Peace
Greenlydia