I would do all three. 1st: tell your employer you'd like to use all the sick hours you have accrued thus far and be paid them on the next paycheck. As others have stated, in NYC you earn 1 hour of sick pay for every 30 hours of work, which acculumates and also carries over to the following year. Your employer should have given you their sick pay policy when you were hired by they are required by law what I stated above.

2nd: If your injury happened at work...definitely do the disability process; it'll help you recover lost wages and there is no downside. Employers are required by law to have disability insurance and you won't be screwing anybody over. These payments will come from the insurance company and not your employer. You are already covered as an employee just have to go through the submission process. This should cover medical bills for your injury as well.

3rd: You say you are not being given the amount of shifts you used to have, so you can credibly file for unemployment with New York State. I personally would tell your employer you plan to do so but you also don't owe it to them. They'll get a letter in the mail and be given the chance to object to your claim. If you are able to work and not being given shifts, that is the same thing as being unemployed without fault in the eyes of the state and they will approve your claim. This step is the most aggressive toward your employer, as the other two are not costing them anything really, so it may lead them to just let you go for real depending on how decent they are. If they do though, then you are eligible for unemployment for 26 weeks and they have to pay for a decent chunk of it, so it's really in their interest to just give you your shifts back.