You didn't have any risk so you don't need to test.
Only sex risks for HIV are penetrating unprotected anal or vaginal. HIV is instantly inactivated in air (which means it is effectively dead so instantly can't infect) so can't infect outside the vagina or anus. It doesn't matter if you were cut where you touched blood, because it is fragile and is not like a cold virus that can be transmitted outside the lungs by coughing.
If it was as infectious as you fear, then all of America would have HIV from people with cuts rubbing them against something that had HIV virus on it, including toilet seats and playgrounds.
The only other way it can infect an adult is from sharing needles then injecting which you didn't do.
All this HIV science is 40 years old and well proven over that time so nothing you can add to your situation will make it a risk.