Vallejo varnishes are well noted for gunging things up.
ALL airbrushes need a total stripdown clean after to get rid of any traces.
Have a good look at the needle as well. It might look clean, but does it feel clean. Try cleaning it off with some cellulose thinners.
If you are having trouble with liquids getting into the trigger chamber, you're going to have to tighten the seal. Most airbrushes allow this. Remove the needle, the needle holder, the trigger and you should be able (just) to see the hole at the bottom where the needle goes. This is where the seal/washer is. A long thin screwdriver a la watch maker will be able to reach it. Check to see that the retaining screw has not become loose.
The needle should pass the seal with a nice snug fit. There should be a little bit of resistance. If it can go though the hole with out any form of resistance, it will need tightening. Just a fraction of a turn will probably do the trick.
After Vallejo Varnish, I always flush with plenty of water, then
airbrush cleaner. I take the tubes and holes with a cleaning brush as well. When I think I got it all, I do it again with cellulose thinner. Its sruprising how much crud there is the second time around. You have nowt to loose, so try giving it a proper clean, inside outside front and back. It could just save you a return and a long wait.
Ian M
PS if the trigger sticks, have you considered removing the air valve and cleaning that as well. And adjust the seal in the needle holder.
