Order you some Airbrush Restorer (made by Createx) Coast Airbrush Products
Plus like AndreZA said use a wooden tooth pick.
You can reuse the restorer over and over again , The bottle I have is 4 years old. and still cuts out dry paint from the nozzle and works on all water based paints.
just soak the nozzle for about 30 minutes to an hour and it is clean...
I seldom find a need to pull the nozzle and clean it, but should I feel it could use a cleaning, I have a cheap ultasonic jewelery cleaner that I'll let it soak in for awhile, but for the most part those tiny nozzles don't need cleaning on any regular basis, if you always backflush several times and wipe down the needle, before you close down the brush for the night.
Best stuff I ever used is SEM's waterborne gun cleaner. You don't even have to remove the nozzle. It has one of those skinny red straws that you can stick right into the bowl of the airbrush and it will flush out everything. Nasty stuff though. Don't spray it in the house. SEM Products :: XXX Waterborne Gun Cleaner