Unfortunately, you can get syphilis from rubbing. If there is a syphilis sore, for example, contact with that could result in transmission through rubbing. Here's a lot of information on syphilis. https://www.webmd.com/sexual-conditions/syphilis#1. If you have primary syphilis, you'd have a chancre sore. They do show up on average at 3 weeks after an exposure (but day 10 to 90 is the time period). Rash for secondary syphilis usually shows up on hands and feet (or other parts of the body) and not until 6 weeks or so post exposure.
An expert at MedHelp, Dr. Hansfield, describes genital rubbing a small risk for syphilis. So, focus on the word small. https://
www.medhelp.org/posts/STDs/Confused-about-genital-rubbing-risks/show/1884295
If you are concerned you have syphilis which I'm doubting you do but no one on the internet can know, I'd go to your doctor for an exam. They can tell pretty quickly. Lots of times by just looking at you but there are also tests. https://www.webmd.com/sexual-conditions/syphilis-diagnosis And it is really easy to treat these days.