Every case is different. Did your lawyer attempt to reach a settlement before filing a lawsuit? That can take months. Once the case is put in suit, it can take several years to get through discovery and through the various court pre-trial conferences before getting a trial date.
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.