My goldfish is sick: red fins, crooked tail. What should I do?

This could be a bacterial or fungal infection. If there are other fish in the tank, trauma cannot be ruled out. if there are other fish, ideally Tiny should be removed to a quarantine or hospital tank for treatment.
If not, you can treat Tiny in the main tank. First, confirm adequate water quality. You can use a home test kit or submit a water sample for testing. The local Petco may offer water testing for free or for a small fee. Aim for an absence (0ppm) of ammonia and nitrites with nitrates at 20ppm or less. perform partial water changes, no more than 30% total volume at a time, using conditioned and temperature matched water. Goldfish are cold water fish that do best between 68 and 74 F. The filter should be rated for at least twice the volume of the tank. Plain aquarium salt (NOT table salt) can be used to reduce stress, treat minor infection and aid in recovery. Dissolve 1 tablespoon of salt per 5 gallons in a cup or two of two of tank water and gently pour it in. Treat for 10-14 days then perform water changes to reduce salinity. Only treat the amount of water being replaced.
More often than not, pristine water quality will allow recovery of minor infections or trauma. If necessary, you can use a broad spectrum antibiotic or all in one product, such as LifeGuard (Tetra) or All In One Remedy (Marineland), to treat the tank. You can find these products in the Aquarium section of the local Petco or online. Follow label directions carefully and remove the carbon filter insert during treatment.