Welcome to the forum. Thanks for your question.
The HIV blood tests are among the most reliable and accurate of any diagnostic test for any medical condition. Therefore, test results always overrule exposure hisotry and symptoms: no matter how high the risk (yours was lower than you might think) and no matter how typical the symptoms might seem for a new HIV infection (yours are not), the test result rules as long as the test was done sufficiently long after the last possible exposure -- as yours were. The bottom line is that for sure you did not catch HIV.
To your specific questions:
1) Your tests are entirely reliable. It takes less long for definitive testing than commonly believed; see the thread linked below.
2) Mo medicines have any effect on HIV test reliability, except possibly potent cancer chemotherapy and immune suppression drugs. Your antibiotics have had no effect on your tests.
3) No, these symptoms do not even hint at HIV. However, if the rash you describe keeps returning despite whatever lotion you are using, I would recommend professional evaluation.
4) HIV doesn't do anything like this. If this is new to her, regardless of lack of itching or soreness, she should be professionally checked. But if she is confident it's nothing abnormal and isn't concerned, you shouldn't be worried either.
I hope this has helped. Best wishes-- HHH, MD