I have a 15 amp electrical outlet in my garage. I unknowingly plugged a refrigerator that required a 20 amp outlet into it and the outlet stopped working. Can I buy a 20 amp outlet and just install it to replace the 15 amp electrical outlet or doea it require some modifications.

They may mean Use on a 20 amp breaker. In the recpticle, it should show damage.
Would do 20 amp recpticle, If you lost power and no sign of damage at recpticle, check for power at breaker and at nearby GFI's
Also if the wire is #14 use 15 amp MAX,
For 20 amps use #12 and
For 30 amps use # 10