I was pushed by my parents to go to college where I earned a Bachelor of Science in Chemistry.

I'm interested in the field, of course, but in a few select areas. So, as I search for jobs, I keep drifting to trade listings which are far more numerous and seem better suited to my style which makes me question if I was put on the wrong path. I don't have the skills or experience and can't afford to go back to school. How do I convince companies to give me a chance? I realize that I'm not going to be very useful without training, but I'm a quick learner... This is where I get stumped. Anyone can claim such a trait, so how do I make my case?