Red is the town doctor of Big Town, and one of the two surviving prisoners from the "Big Trouble in Big Town" quest.
Along with Shorty, she is being held captive in the Police Station to the north of Big Town. Saving her is mandatory, while saving Shorty is (technically) optional. After escorting the two (or one) of them back, she rewards the player (or not, if the player is particularly goody-goody), and can also be persuaded for some bonus caps with a speech check (but success will result in bad karma). The player is then prompted to help defend the town against a two wave Super Mutant attack, but not for an additional reward, other than the end to the quest.
Red acts just like any other doctor in Fallout, and can trade for medical supplies, heal the player, and remove radiation. She offers the player no discount, despite having been rescued by him/her.
Sticky claims that Red is his girlfriend.