Having the virus doesn't have anything to do with wearing a tampon. But the last time I wore one, I got an infection, not because it didn't wear it right but because the menustral blood was caught in my cervix. They had to suck it out woiith a vacuum thing. So if you want, ask your gyn. For more info.
There are more than 130 types of HPV out of which 40 are sexually transmitted. HPV can cause genital warts and some HPV are high risk to cause cervical cancer. There is no harm to wear a tampon or pad if you have HPV but change it frequently.