Can someone tell me if I can form a labor union or something similar?

I work as an independent contractor for a company. My job, and the job of about 500 here locally, is to make deliveries for this company. We are paid per delivery but if there are any problems, even ones beyond our control, we are penalized substantially. I feel it is time for us to be organized and have some representation but I am not sure where to begin. I also have the concern that if the company even suspects I am trying to organize the others they might terminated my contract with them BUT it might be worth it. Can a union be formed or is that only for employees of a company? Collectively, many of us feel it is time to be organized but no one has yet to step up and do something.