Eight years ago I bought some property with a field that was loaded down with thorns of some kind.. I didn't know this, and the first year as I tried to mow this place,, I had tires going flat everywhere each time I mowed.
What to do ? I went to my shop and dug out some sheet metal screws.. I got out my jar of permatex (brush on engine gasket sealer). I picked for each hole what seemed to be a healthy size screw and brushed the threads good with permatex and got my screwdriver and installed the screws into the holes in my tires... I aired up and went back to work thinking I had at least made a field repair to keep going..
To this day, I've never done anything else and I'm still running these tires..
One day about a year later my dad was at my shop and he said uh oh Bill, you have a couple of screws stuck in this tractor tire..
I said, Yeah it's on purpose.. He just grinned and shook his head...
I'm posting this as an idea popper in case you ever find yourself with a small hole and need a fast fix..