Just have a standard syphilis blood test, if not yet done; it will be reliable if done at least 8 weeks after acquiring the infection or 2-3 weeks after the oral ulcer. In the entire US, fewer than 5000 new cases of syphlis occur per year, except in gay men--so on that basis alone, the odds are very low. But to answer your specifc question, syphlis this recently acquried would not cause those symptoms. Accelerated secondary syphilis is extremely rare; the only case I have ever seen was in an HIV-infected gay man, and even it was not as rapid as one week.
Good luck-- HHH, MD