I get many of nails and screws the only time the pose a issue is when they get in the side wall.
Some say you can repair the side wall but for me I wouldn't, plug or patch is a acceptable fix patch is much better and the plug requires some one who knows what they are doing with them.
In ether case you should rebalance the tire.
I don't think anybody has answered your question, take the tire to a Goodyear shop, they'll know more about fixing the tire than most dealers, and I think you'll find it's at no cost. [Most big tire sales stores (chains) will fix flats free.]
They will plug it. There's always a possibility that the tread could seperate using a plug. Put it on the rear. I had a flat on my Liberty, got it plugged and it developed a noise which is air getting past the plug into the tread. I took it off the front and spared it. Patching it from the inside is the real way to fix it but you will be charged dearly for it.