If you're using a cheap airbrush, I can promise you that that is definitely part of the problem. Add in cheap paint not designed for airbrush use, and you're pretty much ensuring that you're going to make things much harder than they need to be.
My default recommendation for new airbrushers is the Iwata HP-CS. It's tough, easy to maintain and clean, it's a workhorse, and is also a very capable airbrush. IMO, it "does it all" better than any multiple-tip airbrush packages I've used, and it does it without the hassle of needing to switch out the nozzle and needle. For whatever reason, I've found that similar, competing airbrushes like the Devilbiss DAGR, Paasche Talon, etc just don't work as well, and tend to have more issues over time.
Plus, the HP-CS is a brush you don't really ever out-grow. You'll probably eventually want to add a specialized detail brush with a smaller tip, and a siphon-feed with a larger tip for larger areas, but the CS is plenty good enough to handle the other 80% of airbrushing duties. Craig Frasier likes to point out that, even with all the access to any gear he wants, he still uses his HP-CS for 90%+ of his airbrush work (although I think he uses the Kustom edition now, which makes sense since he helped develop it).
Com-art isn't really my paint of choice, but it will be a big improvement over the cheap model paints. I prefer E'Tac EFX or Wicked detail, but you could certainly do much worse than Com-art. Just be aware that it WILL tip dry, so get in the habit of cleaning your needle tip often. All paint will give you tip dry. It's simply a matter of physics. Some are just more prone to it than others. I'd say Com-art is about mid-pack when it comes to tip dry. It will happen, but as long as you're aware of it, it's not that big of an issue.