Welcome to the forum. Thanks for your question.
The quick answer is that most likely this isn't syphilis. However, it's possible and you should be professionally examined ASAP, preferably before the lesion heals completely.
You don't say where you are, but heterosexually transmitted syphilis is rare in the most of the US, including in sex workers. And as you suggest yourself, the initial sore of syphilis (the chancre) usually doesn't clear up so quickly. And as you seem to know, it doesn't have an entirely typical appearance. Also, you don't describe a swollen lymph node nearby (e.g., under your jaw or ear, or the neck), which would be typical of most primary syphilis. OTOH, the exposure certainly could have resulted in syphilis if the sex worker has it; the timing, about 3 weeks after exposure, is perfect for syphilis; and a painless lesion also is typical.
Another issue is whether or not you have, or have had, similar lesions in or around the mouth. Although not typical for the chancre of primary syphilis, it looks very much like it could be a "mucous patch". These are a superficial sores of mucous membranes, like the inside of the lips and mouth or the female genital tract and are a sign of secondary syphilis, typically appearing 2-6 months after the initial infection. If have had other extramarital exposures in that time frame, conceivably you have had syphilis for a while. (I assume you don't have any sort of skin rash -- but let me know if you do.)
All things considered, based on the information provided so far, it is unlikely you have syphilis. But not so unlikely that you can safely ignore it. See a doctor about it ASAP. First try your local health department STD clinic, especially if you're in a major metropolitan area. These days health departments are just about the only medical services provide on-the-spot diagnostic tests, and often have the only providers highly familiar with the disease. And in the chance you have syphilis of any stage, the health department will need to be involved eventually, to help identify, locate, and evaluate and treat your commercial partner, and other partners possibly at risk.
As for as your own family, don't do anything yet. Most likely you don't have syphilis; and if you do, "superficial peck" kissing carries little or no risk. But with an oral lesion (perhaps especially if it turns out you have secondary syphilis with a mucous patch), I can't say the risk would be zero. But cross that bridge if and when you come to it. There's no need to 'fess up unless and the diagnosis is confirmed. They will be at no increased risk from waiting.
Please fill in any additional information implied above or let me know if you have any questions. Also please plan on returning with follow-up comments to let me know the outcome after you have been professionally evaluated. (I'm not going to hold you to the forum's usual policy of only 2 follow-up comments or questions.) In the meantime, don't panic. This is conservative, play-it-safe advice, and I genuinely expect it won't turn out to be syphilis.
Best wishes-- HHH, MD