Presumably it was some kind of auto shop that put the snow tires on? You really need to just take it back to them, report the symptoms, and have them drive it.
I suppose unless you are now ~280 miles away in which case run it into a local tire shop. Most anyplace should give it a quick courtesy check.
If you're feeling ambitious, pull out the owner's manual, and follow the instructions for jacking it up (as if you had a flat). Jack up the rear wheels one at a time and spin. See what you can figure out. Do not miss the part about blocking the front wheels, and do not miss the part about not getting any part of your body under the car while it is only on the jack.