I tried to run a little air compressor through my cigarette lighter socket. Turns out that blew the fuse. The compressor uses a bit over 200w. Now the fuse to the lighter is a 20A. 20A x 12V should allow 240W through there which would be about right on the threshold of what I need and apparently not enough. Would it be alright if I just used a 30A fuse there? 30A x 12V = 360W which should work better.

Never just use a larger fuse. You're popping that fuse for a reason...

If you up the size of the fuse... the wire will melt, instead of burning up the fuse. You'd need to upgrade the wiring to support the larger fuse.

Burn up the car... bad idea.