The first question that has to be answered is whether you were an "employee" of the company. All employers are required to maintain workers' compensation insurance to cover an employee injured in the course and scope of their employment. If the employer did not have workers' compensation insurance, the employee can sue the employer for negligence and in fact there is a presumption that the injury occurred as a result of the employer's negligence.
If you were not an employee, for example if you were an "independent contractor", then the requirement of workers' compensation insurance and the presumption of negligence if there was no insurance will likely not apply. In that situation, you may have a claim against the company for negligence.
Either way, you should try to get medical care for your hand. It is probably a good idea for you to consult an attorney who specializes in workers' compensation and/or personal injury to help you figure out what to do. You should do this immediately so you can get medical care and so that your rights are not lost due to the passage of time.
If you are an employee the employer must carry workers comp insurance and must provide you with that information within 24 hours of your demand.
You may contact an attorney handling workers comp in an area and he may be able to assist you to obtain medical treatment through your employer or on a lien. There are many technical issues in workers comp. that a lawyer can help you.
Assuming you are an employee and it sounds like you probably are, then the employer should have given you a workers' compensation claim form right away. That they didn't and that they didn't want you to go to a doctor tells me that they probably didn't have the required workers' comp insurance.
Their not having this insurance will make things more difficult. I recommend you go to the local office of your Workers' Compensation Appeals Board and speak to the information and assistance officer there. They can get you moving in the right direction on this. Later on, you may want to consult with a good w.c. attorney.