I hear this question frequently from my clients and the answer is, "Yes." There is a red in every palette. Women who tell me "I can't wear red" most assuredly have never found the "right" red.
Like every color, red comes in many shades. There are pinkish reds, which have a blue undertone; there are orange-y reds, which have a yellow undertone; there are brick reds, which have a deep golden undertone; and there are true reds which are generally balanced between warm and cool undertones and are therefore, somewhat neutral.
Watermelon is an example of a pinkish red.
Most blondes will wear a pinkish red well, unless they are very golden blondes and freckled in which case an orange-y red will be better.
Redheads can definitely wear red and will look best in the warmer reds such as poppy, tomato or brick.
Brunettes look fabulous in red and will want to wear deep, strong "fire engine" reds or the cranberry shades.
Those with gray hair need to determine whether their hair is a warmer or cooler shade of gray. (Blond-ish gray is warmer; ashy or silvery gray is cooler.)
If the gray hair is warmer, opt for the orange-y or brick reds and if the gray hair is cooler, choose the pinkish reds.
Choose your best red lipstick to coordinate with your color palette. If your best red is a "cooler" red, try Image Matters Red Carpet. Infared will be more neutral, and Red Hot Mama is a "warmer" red.
If you feel like you are "all lips" when you wear a red lip color, try using a red lip pencil with your favorite lip color and your lips will look more "reddish."