I've seen both surgeons and patients claim that the brain usually rewires itself eventually. At any rate, in my case it was true; within a few days the nerves were remapped to their current locations, and I no longer had any sense that the old equipment still existed or was related to what I have now.
And yes, the genital dysphoria vanished the moment I woke up from anesthesia. It *helped* once I actually perceived myself as having a vagina and vulva, but I hated what was there so much that just having it GONE was enough at first. Every once in a while, to this day, I'll touch myself down there (in private, obviously!) just to reassure myself that it really is fixed.
One thing that may help you, and that did help me, was explicitly sitting down with a mirror from time to time and watching as I explored my new anatomy; somehow, actually seeing what I was touching seemed to help my brain figure out what nerves were reporting from where now.