Are there some natural cures for a sore throat that are vegetarian?

No: Sore throats are usually caused by viruses and get better on their own. There are no cures, whether natural or "unnatural." strep throat also gets better on its own, but antibiotics are recommended to prevent rare complications such as rheumatic fever. I don't know of any "natural" way to prevent those complications. Most of the time you'll do fine without treatment, but better safe than sorry.