What happened to the good old fixing your tires after a puncture? I got a puncture the other day, went to a tire place, and all they said was that they needed to replace it. Ridiculous. I had to pay 75 euros for it. If the threads of the tire are still good enough, why is repairing the tire not an option any more? Do you understand this whole thing? I don't.
You went to the wrong place. Try another tire shop.
I had a tire plugged recently in a matter of minutes.
As stated above, can't be in the sidewall.
If you're a do it yourselfer, you can actually buy a plug kit for flat tires at your local parts store. They come with what looks like an oversized crochet hook, and some rubber cylinders and glue.
And Gipper is right, you can only repair a tire on the tread, sidewalls cannot be fixed.
Fix a Flat works in some cases if the puncture isn't too big.
And.................if the tire shop you go to says that they won't fix it, go find another. If you find a family owned type shop, chances are better there that they will fix your tire than large tire chains owned by conglomerates.