Mazal tov on your upcoming wedding!
It is preferable to take most
birth control pills at the same hour each day. You should therefore take the pill at your regular time on the day of the wedding as well. If you are able to take it without water, that is preferable. If not, since this is a
minhag ;and a personal fast, you may take it with the minimum of water needed to wash it down.
Vidui is the only addition to your tefillah on your wedding day.