If you request a hearing now it would probably be set for April, but the first setting almost always get postponed. I would suggest you consult an attorney. If you are entitled to a second opinion and/or change in doctor, you can probably obtain that without a hearing.
You will still need to file it as a workers' compensation claim against uninsured employer. If your attorney cannot resolve issues or settle, you will need to obtain an award from State Board of Workers' Compensation and then convert into a judgment.
You need to report your work injury to the workers' compensation carrier. The workers' compensation carrier should be paying for your medical treatment. If you can save your sick time, I would do that and use WC to pay weekly benefits (provided you are entitled to them).
I would need more information but if your adjuster has assigned a nurse case manager, you can almost always get her off your case. She is not there to help you as you may be led to believe; she works for the insurance company and will talk to the doctor to get you off workers compensation sooner than later.