Tonsil stones and canker sores (aka aphthous ulcers) are two very different things so the treatment is different.

I suffered from really bad canker sores for many years. They can be debilitating! I had one that was so big one time that my doctor took a photograph of it to use in an article he was writing on aphthous ulcers. So one of my sores is famous in some academic journal, LOL. One thing I used that helped the sores was a kind of non-water soluble paste to cover the sore to give it some protection while it healed. Your doc can prescribe it. But the thing that worked best for me was something I discovered later from my dentist--to brush my teeth with a "natural" toothpaste. Apparently a detergent compound in regular toothpaste can cause (not just irritate) the sores. (This compound is sodium dodecyl sulfate, also known as sodium lauryl sulfate.) I switched to using a natural toothpaste about 15 years ago and it was like magic--no more sores! I had been plagued by them for 25 years and switching toothpastes made them leave me alone forever. Yay! Very simple solution that worked for me. The kind of toothpaste I use is Tom's of Maine spearmint flavor. Other natural style toothpastes without SDS would work too.

Note: aphthous ulcers or canker sores can appear similar to mouth sores caused by herpes virus or bacteria, but they have a different cause and are not infectious.

As for the tonsil stones, if they are a continuing problem, I wonder if your doctor would consider tonsillectomy? We don't really need our tonsils. If you get your tonsils removed, the stones cannot grow again on your tonsils, because you no longer have any, so I don't understand what your doctor meant. A tried and true remedy for sore throat is gargling with salt water. That might help with prevention too, as vigorous gargling action might help dislodge bacteria and dead cells that are piling up to form the stones.