So first, I'm sorry you're going through all this.
Since you tested positive on the HSV1 test a couple of days after the encounter, that is almost certainly a pre-existing oral hsv1 infection.
The IgM is an absolutely unreliable test. My own were positive when they should have been negative, and neg when they should have been positive. They are supposed to look for "new" antibodies, and by January, they would have dropped off for you, so it was pointless to do it for you then anyway.
If you had a genital hsv infection, and the presumption being that you had internal sores causing this pain, at some point, you'd get relief. Outbreaks heal.
You do not have hsv2. The test is definitive at 12 weeks.
Also, you didn't have a risk for it. All you did was get a handjob, right? There's no risk for STIs from that, even with spit.
Even if the IgM was reliable, there's no need to start on antivirals just because you have herpes. That's a personal choice, not a definitive treatment.
You can show your doctor this:
"Immunoglobulin M (IgM) testing for HSV-1 or HSV-2 is not useful because IgM tests are not type specific and might be positive during recurrent genital or oral episodes of herpes (460). Therefore, HSV IgM testing is not recommended."
https://www.cdc.gov/std/treatment-guidelines/herpes.htm - it's about 1/4 of the way down the page.
https://westoverheights.com/wp-content/uploads/2014/08/Updated-Herpes-Book.pdf - the IgM is explained in more detail here, starting on page 11.
Antibiotics would not interfere with herpes or HIV testing, though you didn't have a risk for either one. Herpes is only transmitted through oral, vaginal or anal sex, or heavy genital rubbing/grinding while unclothed. HIV is transmitted only by unprotected vaginal or anal sex.
Here are some posts from our experts (when we had them) that may help -
https://
www.medhelp.org/posts/STDs/Nervous-about-mutual-masturbation/show/2183476
https://
www.medhelp.org/posts/STDs/Mutual-Masturbation-STD/show/1968429
https://
www.medhelp.org/posts/STDs/mutual-masturbation-sti/show/1858544
https://
www.medhelp.org/posts/STDs/Understanding-the-risks-of-mutual-fingering/show/1516796
https://
www.medhelp.org/posts/HIV---Prevention/Vaginal-fluid-on-hand-touched-inside-of-condom-and-head-of-penis/show/1119533 - read this thread thoroughly. There is an excellent explanation about why certain activities are not risks, and why others are.