Syphilis should be easily transmittable through oral only when symptoms are present.
But yeah getting Syphilis test blood at 3 months would be basically 100% correct. Longer the better, but 4 - 6 weeks is reliable as well.
chances are very low but you should test for Ngu and ghonorea to make sure you don't have them. and syphillis test is accurate after 3 months i think not sure.