Hello,
Thanks for the query to H.C.M. Forum.
Redness over tip of penis and burning sensation ( stinging) after ejaculation is an abnormal thing , but this is a natural thing.
Due to erection with full force there is rapid flow of blood in penile veins means full quantity of blood , that's why there is redness.
This redness you see at tip of penis after ejaculation.
As perhaps you have noted that when some one ejaculate semen ,it comes out with full force through
urethra and due to this there is burning ( stinging ) sensation( as urethra is a very delicate and soft structure so sensation , feeling is there).
No doubt doxycycline acts against many sexually transmitted diseases and you have taken full course, so no harm.
As far as concerned about H I V , you are not a patient of H I V , because symptoms of H I V are not related in your query.
Hope I have answered your query.
If further any question I will help gladly.
Best wishes.
Dr. HET.