You should never use symptoms as an accurate marker of HIV. Coughing and a fever could be symptoms of may different things, most likely a garden variety virus. Your negative HIV test is good evidence that you do not have HIV. Technically, a test at 3 months is conclusive, but a negative test at 6 weeks is pretty darn good. If you are going to worry, get tested again at 3 months to be 100% sure.
Good luck,
Em