Here is a cutaway picture of an iwata airbrush the packing screw is circled, if you have paint leaking back into the trigger area, I would recommend taking a flat head screw driver and removing the packing screw you can do this yourself . (you will need one something similar to the silver ones in the picture.)
Take your airbrush apart, if you have had a lot of paint build up in the packing nut area first take a q-tip dipped in cleaner and clean and flush out the packing screw so that you can "seat" the screwdriver and un-screw the nut, take it out, it's tiny so don't lose it. Clean the packing screw and the channel.
I suspect that you will also have to take apart your trigger and clean it out, you probably have paint in it and thats why your trigger is "sticky" . That is usually the case however if you have been using solvent based paint there is a chance that you may have to replace the rubber o-rings in the trigger but if you have been using water based products chances are a good clean is all it needs.
When you put the packing screw back in don't "tighten" it down you can ruin it by doing that, put the screw in an carefully, (don't put your brush back together yet). Just put the needle through the packing nut you want to "feel" some resistance when pushing your needle through Just "some" resistance not too tight! It only needs micro adjustments keep testing it with the needle until you feel that resistance.
Re-assemble the airbrush and it should be fine. The packing nut should not need to be replaced probably just needs a good clean and adjustment.
a good tip to remember is when cleaning your airbrush or removing the needle it's always best to take a dirty needle out the front of the airbrush rather then dragging a dirty needle out the back of the airbrush.
You can soak the nozzle in cleaner and using a piece of twisted paper towel dipped in cleaner, you can clean it out . Some will use a tooth pick, whittle down the tip to a fine point and soak it in cleaner to soften up the wood and clean out the nozzle again being really gentle not damage the nozzle another thing that I like to use is the "GUM" dental picks (pictured) instead of a tooth pick to clean the nozzle.
Hope that helps!