What can I do for my stinging urination without going to a doctor?

Not much. If you are a sexually active female, this could be a urinary tract infection. There are myths that cranberry juice and other at-home remedies treat this, but the only way to get rid of the infection is to get an antibiotic from your doctor. Even if it is not a uti, you most likely need diagnosis and treatment from a physician to get rid of the pain. Drink lots of water to help until you see doctor.
Urinalysis +pyridium. Some labs will perform a urinalysis and tell u if a urinary infection is causing stining. U need antibiotics if UTI present. After urine test u can get Pyridium (phenazopyridine) over the counter at most pharmacies, take 200 mg 3 times daily for up to 5 days. Hope u are not financially constrained from seeing a dr.. Many physicians and clinics provided free care in cases of financial hardship. Like healthtap!