I thought I blew the fuse to my refrigerator/freezer because I had plugged something else into the circuit the fridge was on, then saw smoke billowing out the back of my fridge.

Both the freezer and refrigerator have stopped cooling. It is, however, circulating the air I believe.

Any ideas on how to fix this?

Could you please expand upon that? What can I do to check if it was the relay or capacitor (and what do these look like)?

And is this something I could replace myself for a reasonable price?

I have not worked on appliances before, but am pretty handy.