Thank you for your inquiry. From what we gather from the question, you were asking about whether your cold is a symptom of HIV transmission from unprotected sex with a man six weeks ago, and the accuracy of at-home rapid tests.
From this information given the scenario is determined to be a High risk (There is evidence of transmission through these activities and are the majority of cases of transmission). The scenario mentioned above does meet the three components of the transmission equation. At home tests are good preliminary tests. Although the two tests came back negative, CDC statistics show that up to 8 percent of HIV-infected people who use a in-home test can have a false-negative result (1). Due to the fact that you recently had a high-risk exposure, follow up with a physician is recommended.
As for the cold, there are many reasons why you may have contracted a cold or why it is taking a while to go away. This can be do to stress, or many other factors, and is not conclusive of HIV infection.
If you are continuously engaging in high risk activity there are biomedical approaches such as PrEP and PEP that help lower your risk of acquiring HIV. Refer to your physicians for further information.
Recommendation: Refer to a healthcare provider for HIV testing and for other health related questions.
AIDS Vancouver Helpline/Online
1.) HIV Home Tests