For the most part, no. The Internal Revenue Service doesnt consider settlements and awards income and does not tax them. The exception is punitive damages, which generally do not reflect an expense or impact of an injury but instead punish a defendant for particularly reckless behavior. Because these damages dont reimburse someone for an injury, the IRS considers them income and subjects them to tax.
If you claim your medical expenses as an itemized deduction and then later receive a damage award that includes medical expenses, you will need to pay back the amount of the deduction you took.