You had protected sex, which greatly reduces your chances of syphilis. Also, syphilis is fairly uncommon compared to things like chlamydia.
I don't think the risk is high, and without symptoms, you don't need to run out and test, but if you're at the doctor for anything else, just have them run it and put your mind at ease.
If you've had no symptoms thus far, you probably won't get any out of the blue. Just get the test and put your mind at ease. Again - I think it's unlikely you have it, but since it's curable, why not test and ease your mind?