When this happens to me it’s usually either my paints too thin or I haven’t cleaned the airbrush well enough. There may be paint buildup in the nozzle or on the end of the needle which isn’t letting the needle fully seat in the nozzle so paint is able to leak out when the trigger is depressed.
You didn’t hurt anything by leaving pressure on the airbrush. If paint comes out before you pull back on the trigger, the needle is not sealing against the nozzle. That could be due to crud inside the nozzle or the needle is not seated far enough forward.
Remove the nozzle and hold it up to the light. Look in the back end with a magnifier. You should see only shiny metal inside. If there is something in there, try swabbing it with solvent and a small interdental brush. If that doesn’t clean it, soak it in some lacquer thinner or acetone and probe it gently with a shaved down toothpick.
If the nozzle is really clean, loosen the needle chuck and pull the needle back a bit. Now push it gently forward to seat against the nozzle opening. give it a little twist as you do. Don’t push hard or you can split the nozzle. Tighten the needle chuck and try it again.