You are negative, the test prove that, work with your Doctor for your other health concerns.
Could be something else like eczema. My doctor told me it starts on your hands.
A test at or after 3 months is considered conclusive.
There is almost no chance of receiving a false negative antibody test result after 12 weeks post-exposure since current testing methods are extremely sensitive. Reasons for requiring testing after 12 weeks may include a pre-existing immunodeficiency, receiving medication to prevent an HIV infection (PEP), or receiving chemotherapy for certain cancers.
Previously, older tests were less sensitive, which necessitated waiting a longer time for individuals to develop the level of antibodies needed to produce a reactive/positive result. Current testing methods are much more sensitive, which is why current guidelines state that a negative test result obtained at or after 12 weeks post-exposure is conclusive for no current HIV infection.
Given that your test results show conclusively that you do not have HIV, your symptoms are caused by something else.