The FDA is responsible for approving drugs for sale, but not for monitoring their safety after the drug has been marketed. If you have been injured by a drug that the FDA has approved, you may have a right to recover compensation from the manufacturer or distributor of the drug.
People taking medications who suffer side effects may be able to sue if they can prove that the drug was not tested properly before being released or was flawed in its manufacture. They may also be able to sue if they can prove that the pharmaceutical company or doctor didn't warn them of the potential side effects of the medication.