Are they investigating why your other results are abnormal?
You don't have syphilis - your RPR and TPPA are negative. The testing algorithm worked for you. It's designed to find false positives.
I don't know what's happening in your body. A high CRP means you have inflammation somewhere in your body, and while a high neutrophil count most often means a bacterial infection, it can also react to inflammation, stress, etc.
Continue to work with your doctors to find the cause, but it isn't syphilis. There are some reasons for false positives - autoimmune disorders can sometimes cause those.
Good luck to you.
To be clear, you do not have HIV as you tested negative 4 times. Please tell us what your exposures are to begin with.