The IgM test is not useful to diagnose herpes. He needs the IgG test, type specific.
The syphilis test can become positive anywhere from 9 to 90 days after exposure. I’m quite surprised that the county you live in is not asking you to be treated as a contact to syphilis, even if your tests are negative. As you can see, it can take quite a while for a test to become positive. I’m hoping that they are encouraging you to return for more testing if they are choosing not to treat you at this time.
You could certainly go have throat culture but for me, this does not look like herpes but the quality of the picture isn’t great. An in-person examination will likely be more useful.
Terri