Welcome to the Migraine Board. I am right there with you on the weather induced Migraines. I get hit every time a front rolls through. You are currently on a very low dosage of Topamax. That's good. For me, it was poison, and various doctors/neurologists kept raising my dosage. I was up to 400mg, and one doctor thought I should go to 800mg!!! It gave me permanent brain damage. It messed up my short -term memory, the ability to speak well in full sentances, my ability to spell, basically it messed up all my cognitive abilities, probably for good. I've been off the drug for two years and still suffer the mental disfunctions.
As far as your side effects, the breathing problem is probably not caused by the medication. Hyperventilating is usually cause by stress or a panic attack. It would make perfect sense that you are having these spells, in anticipation or worry of getting a migraine. If you were actually allergic to the medication, you would go into anaphylatic shock immediately, which isn't the case here. I don't think you are on a high enough dosage to be getting dehydration problems yet. You need to stop drinking all that Gatorade, as is has acids in it, which help you think it is quenching your thirst. Just drink straight water. Your stomach irritation should go away. If not, discuss starting Nexium with your doctor.
If your migraines aren't significantly reduced in a short period of time, let your doctor know you want to taper off the medication. It works for some people, but does awful things to other people. Frankly, I don't think it's worth the risk of the side effects.
Let us know how you are doing.