Air Brush Broken

Buy a good-quality AB and you'll actually save money in the end.  An Iwata Revolution, for example, can be bought for $70-$90 and good deals are not hard to find.  Compared to prices of new kits and aftermarket parts, a high quality AB (such as the Iwata HP-C+ or the H&S Infinity) is a bargain because it lasts for decades.  

If you have the time and can keep your eyes on the internet sites for airbrushes, you can really get some outstanding bargains. I recently got a Badger 200-20 for $40, free shipping, from Chicago Airbrush. Some find 40% coupons from Hobby Lobby, same or better at Michaels. My Badger 155 was less than $60, can't recall the business though. Patience pays off.

Patrick  

Try jeweler's screwdriver set or eyeglass repair kit screwdriver.

Sometimes you can unscrew the broken off part with the point of a hobby knife.  A triangular shaped needle file could also work.

Don

You should be able to unscrew the remaining part of the nozzle (little wrench that came with the AB) and get a repair kit from TCP Global. If you're not able to use the little wrench you could file a piece of music wire into a triangular point and use that (force the point into the nozzle opening) to extract (unscrew) the remaining nozzle piece. The next step up in ABs is probably the Iwata Neo. Beyond that, you're in  the $100+ range with lots of options.