I put in the window unit this afternoon & it was blowing cold air. I tried to switch it to 'med cold' and it blew the fuse. When I tried to turn it back on it now only blows on 'cold' as if it were set to fan.

Unit is probably 10 years old (it came with the house when I bought it). Is this something I can fix or do I need a new unit?

Anything can be fixed BUT the cost of fixing a window unit can quickly outpace its value. Especially being 10 years old.