Welcome to HCM.
THE CHANCES OF getting HIV
through the method you said in your history may theoretically possible.
But in practice we din't have any such instance as it was a very remote possibility. Using the same applicator without proper cleaning etc. is not practically possible as the solution may not suitable for the virus to stay for minutes. As it is a very sensitive virus, it will not be viable outside our body fluids.
So you need not worry.
Have A GREAT DAY.