They have to do specific blood tests to determine if you have it. Regular testing done during a check up, for example, won't find it.
Yes, a blood test is needed to find these infections. Hepatitis B is a virus, but syphilis is a bacteria.
If you are concerned that you have either of these, you should ask your doctor for testing.
Syphilis is pretty uncommon, and depending on your age, you may have been vaccinated for hep B.
Is this from performing oral sex on the woman? I really wouldn't worry about this from that encounter.