I'm not a doctor but a sore throat with testicular pain can be caused by Strep B. A severe sore throat is one symptom of strep B.
I had a vasectomy done in 1999. I ended up with a hematoma which was removed two days later during an emergency surgery.
A small hole in the scrotum never closed, told not to worry.
A year later I end up with a sore throat headache and a sore swolen left side of the scrotum. After having been in the local hospital for my urologist to come back from vacation, the left side of the scrotum having swelled to the size of a large grapefruit, split open. I was transferred to the city hospital where I received emergency surgery to have a badly Strep B infected testicle removed.
Due to the severity the scrotum was left open and packed with saline soaked gauze every four hours to let the scrotum heal from the inside out. I spent a week in isolation in extensive care. Very very painful and it takes a long time to heal. 11 years later still having some problems because of it. Pain that does not seem to have a source. Phantom pains. Low testosterone, being the minor problems. The pain is the most bothering effect.
Why do you consider HIV? I'm not sure as to how long it takes for HIV might be detected.
I sincerely hope that it is not HIV.
God bless,
Ron