Do I need to keep my vestos [i.e. do bedikos] if I am taking pills to stop the period from coming?
If these pills have shown themselves to work for you to completely stop your period from coming, you would not be required to do bedikos while on the pill.
See Radvaz 8:136, Shiurei Shevet Halevi 189:23, Be’er Moshe 6:137, cf. Minchas Yitzchak 1:127