Your story is long and I just skimmed it since there are only a few relevant details. You only had oral sex and some touching. You had no risk of HIV and are so safe that you don't need to test.
HIV is instantly inactivated in air and also in saliva which means it is effectively dead so it can't infect from touching or oral activities. It doesn't matter if you and they were actively bleeding or had cuts at the time either because the HIV is effectively dead.
Only adult risks are unprotected penetrating vaginal or anal sex or sharing needles that you inject with but you didn't do that so you had no risk. This sentence is all you need to know to protect yourself against HIV.
Even with blood, lactation, cuts, rashes, burns, etc the air or the saliva does not allow inactivated virus to infect from touching or oral activities. The above HIV science is 40 years old and very well established so nothing you can add will make your situation a risk.
No one got HIV from touching or oral activities in 40 years of HIV history, so likely no one will in the next 40 years of your life either.
The doctors left here years ago. Your situation is straightforward, so it is easy to tell that you had zero risk. You aren't the first person who with a nail fungus who doesn't have HIV, so no reason to think it has something to do with HIV.