Hi.
Thanks for your query and proper history.
The discomfort and pain at the back of the right testicle can be due to
Epididymitis , meaning inflammation of the Epididymis.
Pressure and squeezing indicate that swelling under pressure.
The urgency to urinate and feeling of urine in the tip of the penis is due to UTI,
Urinary tract infection.
I would advise you the following :\
Send the sample of urine for culture and sensitivity , microscopy and routine before the start of the antibiotic to get a proper report.
Get blood:CBC sugar and routine.
Ultrasonography of the abdomen particularly for
urinary system, of the scrotum with color doppler mode also.
Get started with an antibiotic and change over if needed.
Get an opinion of an
Urologist.
Scrotal support
Plenty of oral fluids.
Continue treatment till you are cured of the problems.