Yes. Under Florida product liability law, you can recover damages if you are injured by a defect in a product that rendered the product “unreasonably dangerous.” Since a prescription drug is considered a “product” under Florida product liability law, and since failure to warn of known dangers is considered a defect in the product, you could win a product liability lawsuit if you prove: (i) that you were injured, (ii) that the failure to warn of known dangers rendered the product unreasonably dangerous, and (iii) that this danger actually caused your injury.