Should i put bacitracin on dry skin on vaginal lips?

no: That will cause the mucosal membrane to get drier. See your gynecologist since you are needing treatment and household items should be kept out of your vagina.

Dry vaginal skin: I wouldn't use any antibiotic ointments or cream on anything that isn't actively infected. Plain white petroleum jelly is safe for all mucosal surfaces (including eyes, nose, mouth, and vagina.