A woman is permitted to immerse in the mikveh for the sake of other forms of physical closeness.
HPV is very unlikely to spread via water. Even so, as a precaution, you should arrange in advance to be the last woman to immerse on your mikveh night, prepare at home and bring your own towels. Please inform the staff, so that they can change the water after your immersion or filter it overnight.
We wish you a refuah sheleimah! Please don’t hesitate to be in touch as you work through this issue.