They can do all kinds of damage, depending on lots of things, speed being an important one. Go to the city and file a claim. They don't want you to know they have a fund to pay for stuff like this. Don't give up.
It's possible, but not common. Potholes are more likely to damage your suspension if taken at speed. Check your struts and shock absorbers - if a pothole has been bad enough to damage a tyre, it's probably bent a strut as well, and almost certainly will have thrown your wheels out of alignment.
This post was edited by Slartibartfast at April 10, 2018 7:02 PM MDT