I have been on dilantin now for 45 years, along with various other medications at different times trying to find that perfect mix of tablets for control of epilepsy. I had surgery earlier this year and will start reducing medications early next year,( i'm hoping dilantin will be the first one I reduce).
Having said that, Dilantin can cause you to feel dizzy, off balance or unsteady if your blood levels are to far out of the theraputic range, generally to much dilantin will cause these side affects. As for coming off the dilantin , you have to go slowly ,then whilst you are reducing your dilantin you should be slowly introducing the new medication (if you are going to have medication to replace the dilantin).
I would advise you to speak to your specialist regarding quick increases in dilantin also, like decreasing dilantin , a quick increase will very likely make you feel dizzy,unsteady.
Good luck in finding the right medication to suit you.