Can medication cause mouth sores?

I was put on a new medication about a week and a half ago. One of the possible side effects is dry mouth - which I have. I am constantly thirsty. I'm drinking plenty of water, but now I've noticed that my tongue hurts. Not the whole tongue, just one the sides in the way back by my molars. I've looked, and I don't see any sores - maybe possibly a very small canker sore, but not sure. Can dry mouth, excessive thirst, and new medication be causing this? Oh - I also just switched toothpaste brands.