4 weeks is really early to get the syphilis rash. Have you had any sores on your genitals? That comes first, usually at around 3 weeks, and that sore would last around 3 weeks. It's painless, so you can miss it. After that, you'd get the rash.
The RPR isn't totally conclusive at 4 weeks, but it doesn't sound like what you have is syphilis. The syphilis rash doesn't come and go. Were you tested by a doctor? Did the doctor see your rash?
Did you use a condom with your new partner?
Syphilis isn't that common in most developed countries. I'd be surprised if this is syphilis.