Its likely to be a bug bite
If its very cold outside, please rule out frost bite
Gout usually presents with painful swelling at the base of the great toe.
You may give her Acetaminophen/ Ibuprofen
according to her weight for a couple of days.
If it still persists or hurts a lot at any time- please do visit your Pediatrician
Hope my answer helps you.
Wish your daughter good health.