Be clear, HIV experts are in agreement that HIV Is not transmitted through oral sex. It has a theoretical risk which is different than actual risk. Meaning, it never happens. In fact, it has not happened ever in a single, documented case in all these years that HIV was transmitted through oral sex. Air and saliva inactivate the virus. Furthermore, you can't touch and get HIV through something like clippers. Also has never happened.
The ONLY risks for hiv transmission as agreed upon by experts in the field of HIV is unprotected vaginal or anal sex with penetration or sharing IV drug needles. That's it.
Your situation involves personal contact with an object in air ( clippers, hands, blood, vagina, lips, mouth, etc.). No hiv worries, because you can't get hiv from personal contact except unprotected penetrating vaginal or anal, neither of which you did and you didn't share hollow needles to inject with which is the only other way to acquire hiv. Analysis of large numbers of infected people over the 40 years of hiv history has proven that people don't get hiv in the way you are worried is a risk.
HIV is a fragile virus in air or saliva and is effectively instantly dead in either air or saliva so the worst that could happen is dead virus rubbed you, and obviously anything which is dead cannot live again so you are good. Blood and cuts would not be relevant in your situation since the hiv has become effectively dead, so you don't have to worry about them to be sure that you are safe.
There is no reason for a person to test when they are safe. The advice took into consideration that the other person might be positive, so move on and enjoy life instead of thinking about this non-event. Next time you wonder if you had a risk, ask yourself this question. Did I do any of the 3? Then after you say "No, I didn't" then it's time to move on back to your happy life.
We rely on the opinion of expert doctors so don't pay attention to whatever claims you located on the internet or else we will be here arguing all day.
The fact you think a barber cut could give you hiv indicates a bit of a mental health anxiety issue, so either see your doc for some reassurance or else consider a therapist because if that were a possible way to infect people do you have any idea how many million children and seniors would be infected by now?