Hi, itchiness and a burning sensation around the urethra implies that there may be some form of irritation or inflammation around the area. This may be caused by urinary tract infection, or vaginal tract infection.
Urinary tract infection is usually bacterial, and is not uncommon in females. Other associated symptoms may include frequent urination (due to bladder irritation), cloudy urine, hot or burning sensation when passing urine and even blood stained urine.
Vaginal tract infection may be due to yeast or candida - which can have a whitish discharge associated with itch; or other types of infection such as bacterial vaginosis - which can have a greenish discharge with a "fishy" smell. These infections are not sexually transmitted infections but rather due to an imbalance in the natural bacterial flora of the vagina. Both are treatable with antifungal and antibiotics respectively.
For those who have been sexually active (even for oral sex, although less likely), then there is a need to screen for other sexually transmitted diseases such as chlamydia, gonorrhoea and trichomonas.
Without coming to an accurate diagnosis, I'm afraid over the counter medications may not work that well for your symptoms. A consult with a gynaecologist/ doctor is suggested if the symptoms are persistent or worsening.
