Hi Victoria. Welcome to the forum. It sounds like you might be trying to spray your paint on to fast. If you're using a double action airbrush, try going in light layers and bilding up the colors. As far as regular acrylic paints, I have used them before, but with different levels of success. I thin them with regular water until they are the right consistency, about the same as milk, and then pour it through a filter to trap any large pigment particles so they don't clog the airbrush. I wouldn't recommend this, unless you absolutely have to use to. Airbrush paint is designed to be sprayed through the tiny nozzles and will be a lot easier to work with in the long run.
It might help if you could post a picture or two of the problems you're having so everyone could address them a little better. But whatever you do, don't give up. It is a wonderfully fun and challenging form of art and it can be really rewarding