If it bubbles air into the bottle then there is usually a blockage somewhere in front of the bottle. It varies with the airbrush, but in general take the tip / nozzle off and make sure it is clean and clear. The vast bulk of the time problems like this are caused by dried paint in the nozzle. Look through the nozzle and see if you can see light through it. Clean the path airbrush body thoroughly. If there are regulator holes around the nozzle make sure they are clear (I usually run a fine piece of wire through mine).
If there is a gasket or seal between the head and body that could be leaking and causing air to blow back into the bottle. Some Badger airbrushes have a Teflon washer between the body and head that will flatten over time and sometimes that will cause air to blow back into the bottle.
Assuming that it won't harm the airbrush the best way to clean a tip is to soak it in laquer thinner overnight. Not knowing anything about the airbrush I'd recommend not soaking anything plastic or any o-rings in laquer thinner because some parts can be harmed by it. Don't get laquer thinner in the air valve because there is typically an o-ring in there. Be cautious and use laquer thinner only on steel parts unless you are certain that what you are cleaning is not affected by solvents.
Pipe cleaners, Q-Tips, brushes, etc. are very handy for cleaning airbrushes but make sure you don't leave any lint inside.
As to upgrading, if the brush you have does everything you want then there is no real need to. If your "Asian" airbrush is a Tamiya I think they are made by Iwata. Your choice, of course, but first decide if you will really accomplish anything by doing so. Take a look at this page on my web site:
http://www.craigcentral.com/models/ab.asp
It might be of some help.