What is evidenced by the high urge to urinate during withdrawal bleeding?

Thank you for sharing your case. You probably have a urinary tract infection.

According to the available medical literature, the use of contraception (including hormonal contraception, e.g. contraceptive pills) increases the risk of infection both in the vagina and inflammation of the urethra or bladder. Depending on the ratio between estrogen and progesterone concentrations, there may be changes in the amount and composition of vaginal secretion, which may lead to a decrease in the amount of beneficial lactic bacteria, and thus – an increase in the risk of bladder and urinary tract infections.

Also, sexual intercourse increases the frequency of urogenital infections (women quite often find cystitis after intercourse). I encourage you to read the article:
https://www.gdziepolek.pl/artykuly/zakazenie-drog-moczowych

Within the scope of his competence, a pharmacist may propose over-the-counter products, e.g.:

Urosept herbal preparation supporting urination and the functioning of the urinary tract https://www.gdziepolek.pl/produkty/81022/urosept-drazetki/apteki

Neofuragin - a drug that inhibits the growth of bacteria https://www.gdziepolek.pl/produkty/52652/neofuragina-tabletki/apteki