Theoretically, yes. There are cases like that described in older (pre-WW2) books on syphilis. Oh, those good old days of pre-antibiotics era...
Did i freak you out? Sorry about that.
But realistically, no, your risk is zero. It never happens these days since syphilis is a rare disease and even if your partner was infected your risk would be minimal.
The biggest problem in your case is not syphilis (you don't have syphilis) but your anxiety. Go get tested to snap out of it. Syphilis tests are very sensitive at 6 weeks and treponemal tests are as good as conclusive.