Your answer from the hobbyists is---no, it's not normal and we don't experience this.
Your next answer needs to be from your doctor, seriously. There are many rewarding hobbies, and this one may not be for you. There are a lot of toxins that do exist in this hobby, but your reaction is severe and nothing any of us are experiencing. In any case, make your doctor aware: he may order an EKG and stress test to see if there's an issue outside the tank: any heart problem is usually far easier to head off than to deal with after there's damage; but it could also be respiratory reaction, and that can be serious really fast. Try to find out WHAT it is. None of us can think of any common allergy that could be doing it.
My advice would be to find something else you truly long to do, be it model ships or bonsai or whatever.