Hi.
Thanks for your query.
This is a thing to be concerned about.
The pain in the testicle severe enough to be felt as to be liked kicked in and the referred pain in the lower abdomen can be due to torsion of the testes or severe epididymo-orchitis.
Occasionally this can be due to ureteric colic giving referred pain in the testis.
Hence I would advise you to undergo urgent ultrasonography and color doppler examination of the abdomen and the scrotum to get an appropriate diagnosis and to get a proper treatment as per the reports.

I welcome you to health care magic
I am Dr Fahim, General Surgeon and I will be addressing your health concern
I have gone through your question and understood your concerns. These symptoms guides us towards any calculus in the urinary tract on the left especially in the lower ureter. When stone passes through the tract, one experiences severe colicky pain, which starts, slowly increasing in intensity , reaching a panicle in about half an hour and then subsides gradually. It is usually accompanied by vomiting. You need some investigations ie Urine Routine Examination, Ultrasonography kidney, ureter and bladder, and in some cases CT scan KUB, to help us know about the exact pathology. However if such a patient walk into my clinic, I usually prescribe pain killer and spasmolytic for rapid pain relief. Followed by mentioned investigations.

Wishing you all the best and rapid recovery.
I hope my answer will help you. Do rate my answer if you like it.
Regards