You would of known if the condom broke. Protected sex is zero risk for HIV.
Your hiv free. Dry cough has many possible causes, bacteria or flu virus etc. In terms of cough and hiv, it's caused by tbc. In many cases the body can fight tbc but with hiv it could not be fighted by immuun system. But if that was the case it's only in late hiv stage so not in a few month. Don't use symptoms as indication, test will overrule symptom and proofs it has a different cause.