Welcome to our Forum. Thanks for your questions.  I'll be lad to comment.  As I understand it, the tests that you had on December 1 were 8 weeks following your last exposure on October 6.  If my dates are correct, your HIV test taken at that time provide conclusive evidence that you were not infected with HIV on October 6 or before (even if the test was a 3rd generation test).  The clinical manifestations and course of syphilis are highly variable and nothing about he course you describe is in any way suggestive of co-existent syphilis and HIV. 

2.  You are correct.  HIV test results taken at any time more than 6 weeks after an exposure are entirely conclusive.  There is no medical or scientific need for additional testing.  your doctor is being overly conservative or perhaps has used older, out of date guidance to recommend further testing at 3 months.  Your results will  not change.

I hope these replies are helpful to you.  If there are further questions or any part of my answers above in unclear, please don't hesitate to use your up to two follow-up replies for clarification.  EWH

1.  While the "classical lesion of primary syphilis is a solitary, painless genital ulcer, multiple lesions are not at all rare or uncommon and when they occur they are not a sign of HIV co-infection.  There are no specific symptoms that suggest HIV coinfection in persons with HIV.  For that reason, testing is recommended.  In your case, you have been tested, I urge you to believe your test results.

2.  The phrasing of your question suggests that you have had penile lesions on multiple occasions. This is not typical of syphilis.  If the lesions occur recurrently, or if they recur following treatment for syphilis, the lesions should be tested for herpes using a PCR test on a swab specimen from the lesion.

Syphilis is transmitted through DIRECT contact with an infectious lesion. If your partner had a lesion on his penis, rubbing penises could have led to acquisition of syphilis.  Even brief unprotected penetration can also lead to infection.

3.  The most widely used syphilis test for follow-up of infection is the RPR test.  The RPR test measures the strength of an infected persons antibody response which is report out as a "titer".  Following successful treatment the RPR titer tends to slowly decline over a period of months (6-12) in the majority of patients.  On the other hand, if the value to the RPR titer goes up four-fold or more on repeat testing, it may indicate re-infection.  In this way persistent antibodies can be distinguished from re-infection.

I hope this additional information is helpful.  EWH