This is standard practice. The check will be for the amoun in the release you signed. You will get a little less than 2/3 of that amount -- disbursements come off the top. Your lawyer will give you a closing statement that explains where the money went. Your portion is tax free.
Are you covered by workers compensation? That is the first thing to figure out. Contact a lawyer asap. If you are not covered by workers compensation you need to submit a no-fault insurance claim to his auto insurance carrier within 30 days of the accident to get your medical bills and any lost wages paid.
Ask if the hotel had medical payment insurance coverage. This covers bills regardless of whether the hotel was negligent. In order to sue you will need to prove the hotel had actual or constructive notice of the screw. That probably will come down to what the screw is for, where it was and when the room was last cleaned before the accident.
You have the right to appeal. Be sure to serve and file the Notice of Appeal within 30 days of sentencing. I can not access the likelihood of success on appeal without reading the trial transcript or at least hearing about the testimony in more detail.
It depends if you have a serious injury as defined in the Insurance Law. Contact a personal injury lawyer asap and be sure to submit a no-fault claim with your insurance company within 30 days so your medical bills and lost wages get paid.