As AuntieJessie said, syphilis can be transmitted even when sex is protected, but the risk is lower than when having unprotected sex. By the way, herpes can be transmitted when sex is protected. Did you also test for herpes ? if you did it, and it was 3 months after your exposure, the result would have been conclusive.
Yes, your tests were conclusive. A syphilis rash would be more widespread on your body. It's usually on the palms of your hands, the soles of your feet and your torso, but can be anywhere on your body.
While it's possible to get syphilis from condom-protected sex, the chances are much, much lower, and syphilis isn't that common. I wouldn't be worried about syphilis.
If your rash lingers for a few more days, or spreads, let a doctor see it, but I wouldn't worry about it being syphilis.