Yes, you can get a PCR swab done to determine if your symptoms are due to viral shedding
I don’t know what you mean by inconclusive. Either it is positive or negative. There is no middle ground that I know of on a PCR swab. So I’m confused by that.
Something that last for 2 months is very unlikely to be related to HSV infection.
There is no reason to look for white blood cells – not sure if you mean by blood or by swab? Maybe you mean by swab. If your gyno would provide you with PCR swabs to take home and return after you gather them, this would be helpful for you to know if these symptoms are related to HSV or not.