Welcome to RVF,
@Cameron; glad to have you join us. And, sorry that you're having issues with your refrigerator.
Could you post photos of the plug and receptacle so we know exactly what we are dealing with here? That would help. Someone here might recognize the flag and know of a source.
Most plugs/receptacles are pretty standard electronic components and you might also search one of the online parts houses for a replacement. Here's are links to Digikey and Mouser. Both that sell a wide variety of electronic components. I would be surprised if at least one of them didn't have some kind of replacement. You will have to do a bit of searching to find an exact match, but I've found a lot of "hard-to-find" electronic components on those sites.
DigiKey offers millions of products from thousands of manufacturers, many in-stock quantities available to ship same day. Apple Pay, Google Pay™ & Paypal accepted, order online today!
www.digikey.com
Good luck.
TJ