A missed period alongside thick, itchy white discharge is usually a vaginal yeast infection, which is common before a period. Since you were sexually active about 10 days ago, it is also worth ruling out pregnancy as a reason your period hasn't started.
Next Steps
Take a home urine
pregnancy test today, since it is accurate from your missed-period date. Please see a gynaecologist to confirm the infection and start the right treatment.
Health Tips
Get checked sooner if you develop lower belly pain, fever, or the discharge turns foul-smelling.