If your veset is during the day, i.e. your last period began during the day, and you are observing the night as an onat perishah out of stringency, then you may immerse and even have relations on that night.

If your veset is at night, then you are correct that most authorities prohibit relations even on mikveh night. There is debate about whether immersion itself is permitted for the purpose of other physical contact. Our site's rabbinic supervisor, Rav Yehuda Henkin, permits immersion in this case.