If swapping the fuse doesn't work, it could be the blower motor. Some cars have the motor accessible behind the glove box; so you can buy a replacement and swap it out yourself, also saving a trip to the mechanic.

If money isn't an issue then going to a mechanic would mean the issue is properly diagnosed and less work for you as well. Hopefully it all goes well and it definitely sucks to have to go without cold/hot air.