Unfortunately I managed to put a rather large hole in my carpet from getting in and out of the car with heels on, and not making sure I was stepping on the mats. It's on the right side just above the mat. Any ideas/solutions on how to repair it?

 

I would try to find someone parting out a car and buy the carpet and install it in yours.

 

You could cut a square piece from a hidden location like under a seat and then use a razor knife and cut the damaged section out of the carpet. Trim to fit, glue it in, and brush when dry with a scrub brush.

Then optionally get a rubber truck mudflap, cut to fit and place it over your existing mat for extra protection.