It is possible to acquire HSV 2 after having HSV 1 genitally yes, but not common.
I’m not convinced that all of this is HSV 1. I know you the had one swab tested, but the recent ones, I’m not so sure about with all the itching, could it be fungal? And no, it isn’t usual for the skin to stay so sensitive for months either. Have you tried anything topical on this area at all?
Terri