I regret to hear about your injury and regret even more that I have bad news for you. To claim unemployment benefits, you must be available and able to work. If you are under doctors orders for bed rest and no exertion, then you cannot claim benefits during the time that you are physically incapable of working. If you received no instruction for bed-rest and are capable, for example, of desk work in your normal capacity with no need for convalesence, then you can continue to certify your weekly claim. The statute is NY Labor Law Sec. 591(2) which requires an indiviudal to be able to work in their usual capacity. Pregnant women on unemployment face this dilemma and typically cannot claim benefits when they are incapable of working. Gols v. Ross, 399 N.Y.S.2d 337 (3d Dep't 1977).
Consult with your physician and follow doctor's orders. A job will do you or your family no good if you are dead. Think about it.