Your white discharge with itching usually means a vaginal yeast infection. It can make your urination burn and feel urgent even without a true urine infection, since the discharge irritates the area around your urethral opening. The absence of fever or pelvic pain is reassuring here.
Next Steps
Keep the area clean and dry, and switch to loose cotton underwear instead of synthetic fabric. Avoid scented soaps or vaginal washes, since these tend to worsen itching. A vaginal swab test will confirm whether this is a yeast infection or something else, so you'll know the right treatment to use.
Health Tips
Please see a gynaecologist within the next couple of days to get this confirmed and treated properly. Go sooner if you develop fever, lower abdominal pain, or the burning gets worse.