This answers all of your HIV questions, and if you can think of any more just reread about the 3. You had zero risk therefore testing is irrelevant to your situation because you had zero risk. HIV is a fragile virus, which is instantly inactivated in air and also in saliva which means it is effectively dead so it can't infect from touching, external rubbing 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 3 adult risks are the following:
1. unprotected penetrating vaginal with a penis
2. unprotected penetrating anal sex with a penis
3. sharing needles that you inject with.
The only way to get HIV is if you did one of the 3. The situation you describe is a long way from any of these 3.
Even with blood, lactation, cuts, rashes, burns, etc the air or the saliva does not allow inactivated virus to infect from touching, external rubbing or oral activities. Doctors have calculated the risk from what you describe to be less than that of being hit by a meteor, therefore no one will get HIV from what you did in the next 40 years of your life either. The above HIV science is 40 years old and very well established, so no detail that you can add to your encounter will change it from zero risk.
You don't have any medical training so it is unrealistic for you to think you know how to do the nurse's job and she doesn't. It is also unrealistic for you to think she could have infected many people at work but no one there could figure it out - except you.