No, if you tested negative, that means you don't have it. While symptoms can appear years later, that only happens if you have it.
The testing you had done was likely antibody testing. If you don't have antibodies, you don't have the infection.
Also, you had protected anal sex. There is no risk for HIV or any hep virus with this (or most other STDs).
Loads of things can cause low neutrophils. You'll need to work with your doctor to find out the cause of yours. Depending on how low they are, it may not even be cause for concern, but that's something you can talk to your doctor about.