If you were on the phone and this is documented in the police report, by any witnesses to the accident, or via a conversation you had with the driver of the other vehicle, your insurance carrier will likely want to settle the claim prior to litigation. I am assuming that a lawsuit has not been filed by the plaintiff at this juncture. If the claim can't be settled, your carrier should pick up the costs associated with your defense. Hope this proves helpful.
You should hire an attorney. He may be able to send a letter to the other driver explaining that his failure to cooperate with his carrier will leave him with no coverage resulting in him being personally responsible. This guy needs to be pushed into doing the right thing!
I assume you were provided with a handbook or written guidelines that deal with absences from work and how to file a grievance. Are you a member of a teacher's union? Check available resources and contact a lawyer in your area. Hope this helps.
Do you have the names of anyone who saw you fall? Need confirmation that the carpet was torn. Photos would be great if you have them. As previously indicated you will need to show prior notice of the problem. By the way you were treated by the hotel staff, I would recommend hiring an attorney.
Here you go. See if you can get the medical bills reduced. Try for a 50% discount. Try to get a few thousand more from the insurance carrier. If you are successful, settle the case. If not hire a lawyer.
Have you talked to the lawyer who is currently handling your case? You have to agree to the referral. Look him up on AVVO and do a Google search. Is he board certified? Does he try cases? Do you feel comfortable with him taking over your case? If not, talk to a qualified attorney in your area ASAP!