It depends.  In most cases today, insurance policies contain "subrogation" or "reimbursement" provisions that claim that the insurer can force you to repay if you recover damages in a lawsuit or settlement.  While Georgia law generally prohibits an "assignment" of a personal injury case and disallows "subrogation", it does allow for "reimbursement" if you have been made "whole" for all "economic and non-economic" damages.  The burden of proof is on the health or auto insurer to prove that you have been made whole, which is difficult to do if the case results in a general settlement.

If your "insurance" is through your employer, a federal law, known as ERISA, may trump (or "preempt") Georgia law.  If the ERISA plan is "self-funded", you may be stuck having to repay.  In other words, your "health insurance" acts like a glorified loan of funds, not true insurance.