White discharge along with itching and some swelling near the vaginal opening usually points to a vaginal infection such as a yeast infection or bacterial vaginosis. These are common and treatable. An infection on its own usually doesn't delay your period. A delay of a few days by itself isn't unusual and can happen with stress or minor hormonal shifts.
Next Steps
See a gynaecologist for an examination and a vaginal swab test, since the right treatment differs between a yeast infection and bacterial vaginosis. Keep the area clean and dry, and wear breathable cotton underwear in the meantime.
Health Tips
See a gynaecologist sooner if your period still hasn't started in another week, or if you develop fever, pelvic pain or foul smelling discharge.