Hi Lizagamma!
With any new medication, to give it a fair shot at working would be staying on it for 6 weeks or longer.
With that being said, if the side effects are too severe, then maybe that medication is not right for you. You mentioned you've tried Topamax and Zonegran, both in the anti-seizure catagory of drugs. Have you tried any other catagory of drugs for migraine prevention? There are over 100 drugs currently being used and endless combinations.
If the side effects are too severe on the zonegran, don't be shy about speaking up and letting your doctor know you just can't handle them! We are put on these medications because the good they can do for us will hopefully outweight the side effects. Sometimes this does not happen. In this case, it may be best to try something else.
Usually the side effects will/may lessen in time, about 6 weeks or so. But, again, if they are too severe for you to wait, please let your doctor know.
Good luck!