Am I tanning? If so, how can I stop?

From the wiki

Preventing a Tan

To prevent a tan, go out with an umbrella, don't go out while it's daytime, or stay inside. Drastic measures include Time Travelling or staying off the game for long periods of time. Hats will not stop tans from appearing.

Removing the Tan

• Take precautions. When going outside on sunny days, the player should use an umbrella or anything that will block out sun completely.

• Wait it off. Tans will fade after a while, and with some extra help it should be gone in no time.

• Stay in a building or animal's house for about an hour. Turn the game off and save, time travel to the next day, and then repeat. Keep doing that for a while and the player's tan should eventually start to fade.

Liquefy's FAQ on ACNL also has some additional info.