Hello
Almost 5 weeks passed after sexual ENCOUNTER with a girl .
According to your query , there was chance that PENIS got contact with vagina but without condom .
This is a cause of concern .
The vaginal secretion with cervical secretion are highly contagious and infectious of an HIV infected patient .
Insertion of penis is not necessary for getting HIV , contact of infected secretion with penis tip (urethra ) is sufficient .
Now cough is there but not responding to usual antibiotics , that is also a cause of concern.
Other symptoms of HIV are mild low degree fever,
pharyngitis ,
lymphadenopathy, headache/ tetro-orbital pain, lethargy/ malaise, anorexia/
weight loss, nausea/vomiting/
diarrhea, mucocutaneous ulceration ( tongue coating ) .
In my opinion since 5 weeks passed so get in rapid Western blot antigen antibody test for HIV confirmation.
Because tension and
anxiety also play an important role in cough.
Hope this will help you.
Good luck.