Okay, so how are you being treated? What meds are you being treated with, and what is the dose?
You have secondary syphilis, since you have the rash. You should be getting shots of penicillin, unless you are allergic to that. If you're allergic to penicillin, they'll either try to do desensitization therapy, or treat you with doxycycline or tetracycline for 14 days.
Your levels went back up by more than 4fold - from 1:2 to 1:16, which means treatment failure or a new infection, since they had already dropped by 4fold, from 1:64 to 1:2, which indicated you were cured. I'd have to think you were exposed again, but your girlfriend is being treated AND testing negative, which makes that seemingly not possible.
What kind of testing are you both having done?
There is an incredible doctor who is probably the world's expert on syphilis, Dr. Edward Hook. He answers questions on ASHA - http://www.ashasexualhealth.org/experts/ He literally wrote a textbook on syphilis. You have to pay to ask him a question, but since this is a really tricky case, if you can afford it, I'm suggesting him. You can click on Premium Services on the above link, or get to it here - https://www.askexpertsnow.com/
I'm happy to help however I can, but he's a lot smarter than I am. If you do post there, title it with Syphilis in the title, and I think he answers all the syphilis questions.
Let me know what happens.
What are your doctors saying about this? What kind of doctors are you seeing? If you aren't seeing an infectious disease doctor, you should be.
Your HIV test is NEGATIVE several times, and that is a very reliable test, nothing influences it's acuracy. Have no worries about that, you are HIV negative.
You gotta make sure you got adequate dosage for the syphilis stadium. Usual dosage is Benzathine Penicillin 2,4 million units, 1,2 in in each buttock. You probably got that.
It's also possible to give 1,2 million units daily for 10 days, so longer, that is a good option.
If it was me, I wouldn't repeat the same regimen of MU 2,4 twice, when it might have failed once.
Penicillin is usually the best and experienced doctors swear by it, but also Doxycycline, Ceftriaxon, Azitromycin can be used.
You need a good specialist which will give you stadium adequate drug and dosing to make sure.
Diarrhea is not a particular symptom of Syphilis, and rash of Secundary syphilis is most often dramatic, obvious rash on body, or palms. Not some rash on wrists.
You'll see the tests next time, these symptoms don't sound like syphilis, but lab will show.