Fix it first
Tire Repair
Where the damage allows it, a puncture gets repaired instead of replaced. The sensor gets relearned afterwards, so the light on your dash actually goes out.
When a repair holds and when it doesn't
A puncture straight through the tread, away from the shoulder, is usually a fair candidate for a proper repair. Anything in the sidewall, anything near the shoulder where the tread curves into the sidewall, or a tire that's been run flat isn't a safe repair no matter how small the hole looks, because the internal structure has already been damaged in a way you can't see from outside. We check the inside of the tire off the wheel before we tell you either way, not just the outside.
Bailey's Tire Service, walk in during opening hours for a puncture check. Call (985) 876-5082.

A proper patch-plug versus a plug alone
A plug pushed in from the outside seals the hole, but it doesn't address the inner liner, and it's not something we hang our name on as a finished repair. A patch-plug combination goes in from the inside: the tire comes off the wheel, the puncture channel gets cleaned and filled, and a vulcanized patch goes over the inner liner to seal it properly. It takes longer than a roadside plug because the wheel has to come off, but it's the repair that's actually built to last.
The TPMS relearn is the part that gets skipped at a lot of quick-fix shops. Every sensor in the wheel talks to the computer at a specific pressure baseline, and breaking the seal to repair or remount a tire can knock that baseline out even when the tire itself is perfect. Our hiring paperwork lists TPMS relearning procedures and wheel torquing procedures as named skills for exactly this reason. Skip the relearn and the dash light stays on, or worse, comes back on a few days later for no reason you can see.
Torque matters just as much as the seal. A wheel put back on too loose can work itself out on the highway. Too tight and it can warp a rotor or crack a stud over time. We torque to spec, in sequence, every time a wheel comes back off the car.