I carry a Stop & Go tire plug kit with all the time for emergency...but if I were to be home and have a small nail or similar object in a tire, I may be tempted to hot patch it from the inside....
It can be done, know some that have gotten good mileage from a patched tire...but I'm not recommending this practice...at you own risk....
I have successfully plugged my rear tire and still used up the remaining tire life. Since then, I found a product called "Ride-On". You put it in your good tires and if you find a nail, you pull the nail then ride. The hole is sealed by the product. Another beneficial side-effect is that the product balances your tires. If you do a search, you will find that a lot of people here would recommend Ride-On.
I carry a plug kit but will replace a plugged tire as soon as possible regardless of the milage. prol overkill, i know some folks have riden with plugged tires for the life of the tire but i don't feel comfortable doing that. we only got 2 tires on the road.....
What you need is called a plug-patch. It looks like a big roofing nail, and requires dismounting the tire to install from the inside. Dunlop refers to it as one of two approved ways to repair a flat. I recommend you look at the Dunlop website for info on flat repair.