"A girl in red" is the best sentence. "A girl in the red" as other meanings. " A girl in a red dress" is the correct full correct sentence, "a girl in red" is used informally colloquially

The girl in red is my daughter. The girl wearing red is my daughter. The girl dressed in red is my daughter. The girl in the red dress is my daughter.

Firstly "the girl in the red" is not correct English, you would need to add the word dress to the end to make it natural... "The girl in the red dress". You might want to know that the term "in the red" is used to refer to being financially in debt. So either using the full "the girl in the red dress" sentence or your other example "the girl in red" would both be good to use.

A girl in red