What can cause a 16 month old girl to cry and hold her vaginal area?  doc won't test for UTI since no other symptoms. No redness or swelling in area

Vulvovaginitis. Inflammation in the vaginal area is known as vulvovaginitis. It can be caused by chemical irritants, bacterial/yeast infections, trauma, etc. A mild non-chemical cleanser (colloidal oatmeal, aveeno) and acidifying the bath water (vinegar) may help calm the irritation and promote healthy protective bacteria. If she has a fever or vomiting, ruling out a UTI would be reasonable.
Uti or vaginitis. Painful urination is most commonly associated with urinary tract infection. Other causes may be local irritation of vagina due to chemicals (ie. Soap) during bath/wiping or from poor hygiene. Use cotton balls with water only to clean when soiled and avoid harsh soaps during bath. If discomfort persist or any pain/fever, then insist on testing urine for infection.