When I was diagnosed 4 years ago I never thought I would be alive today, but here I am and life is good. I think I could have been diagnosed when I was first infected. Go with your gut. I hope that you are wrong. But get tested.
Nothing can irradicate the virus, really.
There is this controversial study about starting antiretrovirals and help the immune system fight the virus as soon as infection occured but it hasn't been approved as the best way going forward yet. There are many people with complex phobias or simple lack of knowledge about these and other issues, so sometimes the best way to put their minds at rest is for them to have a chat with a skilled health professional who would be able to explain the risks and their level. Getting tested after each cut is crazy. Especially, if one cannot contract HIV in a particular way in the first place. Some hair establishments can indeed be dirty but the virus does not live outside the human body so transmission is not possible in principle.