TCA easily kills the warts (and anything else it gets on). A tiny little drop on the wart and it will die and be gone with no scar in less than a week. HPV is caught through sex. I don't know how long it takes for warts to reveal themselves after contraction.
You are so wrong - you can carry the virus for years and then develop it when your body or you are under stress - you do not have to be promiscuous to get genital warts, that is just silly. There is an essential oil called Tree of Life, which can be used to treat warts but diluted with carrier oil, for massage (similar to Tea Tree). The tincture of this can be soaked in a tampon and used to treat internal warts but be cautious when doing this as not to burn the skin.
Make sure you are consumer lots of vitamins especially B & C, eat well, get lots of rest and be good to your body to encourage healing.
Don't worry, it is not serious. Also, the good news is that you onlyhave a small afflicted area. TCA is a good option. It destroys the virus proteins, without causing any deep damage to tissue. The doctor will use 90%. The higher %, the deeper it goes, so you should only need one treatment. It is possible that you will need to return for further treatments. The skin will turn white with application and then it will look like sunburn. You probably will want to not wash it off for 48 hours. The dr will probably protect the surrounding skin with vasolene. A baking soda paste can also be used. People that use TCA at home should have a baking soda solution on hand to neutralize any accidental spill or for getting it on healthy skin. The good news is that TCA is the quickest treatment for most people and it is the cheapest. If you were prescribed Aldera cream, for example, you would have a big co-pay.
You might want to ask your doctor about vaccines for the most common HPV's for the future. There are several other different HPV's. The vaccine is dead viruses that build an immediate immunity in your body, to not allow them to infect.