I can relate to your condition. I have had two nails (one in each rear tire) in a short timeframe. I had to replace one tire because it was not possible to repair. The other tire I was able to repair. The factor to consider is how many miles you have on the set of tires that is mounted on the car. When I had to buy a new tire I had about 8,000 miles on the set. When I mounted the new tire the car felt out of balance due to differential of rear tires circumference.
You may take it to a tire repair shop and have them take a look where the nail is and see if the recommend replacement of the tire or if they can repair it. All this said, it is stated in the user manual that tires are not to be repaired in the event of a puncture.
I looked on the Bridgestone site for information regarding repair and eventually wound up at tiresafety.com which appears to be related to Bridgestone and Firestone. Good luck.
Repair of Speed Rated Tires
Tires that are speed rated may be repaired with the following procedures; however, these tires would no longer maintain their speed rating.
Determining if the Tire is Repairable - Limits
* Never repair a tire worn below 2/32"(.16cm)
* Never repair tires with tread punctures larger than 1/4"(.635cm)
* Never use an inner tube as a substitute for proper repair.
* All repairs must be made from the inside of the tire as well as outside.
* The maximum number of nail holes is limited to two per tire and these must be separated by at least 15"(38cm).
* No more than one cord per radial ply can be damaged.
* Section repairs are not allowed.
Inspection Procedure of a Service Professional
* Mark injury and remove the puncturing object.
* Before deflating, immerse the entire tire in water to determine if there is more than one hole.
* Remove tire from wheel.
* Inspect puncture with blunt awl to determine size and type of injury.
* Place the tire on a spreader and inspect thoroughly.
If any of the following conditions exists, the tire cannot be repaired:
* Holes larger than 1/4"(.635cm)
* Run flat damage
* Broken or deformed bead wires
* Ruptures of radial plies
* Deterioration of rubber
* Damage to the bead
New valve stem, core and cap are recommended for all new tubeless tires.
Tire beads and rim flanges should be treated with a recommended lubricant inside and out. Beads should be lubricated both during mounting and dismounting (in case you wish to remount the tire and also to protect the wheel from damage).
Do not, under any circumstances, use liquids such as oil, gasoline, spirits, or water.
I had a nail puncture after only 200 miles on new rears. It was in the outermost block. Could not patch. So, another new tire. I now have the tire insurance that covers replacement for the next 5 years pro rated for wear.