Unfortunately in most premises injury cases, the negligent party will not have insurance to immediately cover your medical expenses. However, it pays to ask, as some negligent parties will carry coverage known as Medical Payments coverage which will pay your medical expenses (usually up to a total of $5,000.00 – if it is carried at all.) In the event that the negligent party does not have Medical Payments coverage, you are going to have to fend for yourself until such time as you can resolve your claim against the negligent party. If you have group health insurance--or Medicare or Medicaid--you should be able to access health care, but you will need to be prepared to reimburse each of these payors at the conclusion of your claims.
The negligent party may eventually be made to answer for all of your medical expenses, but this will not occur until you are prepared to resolve your case in full (which is usually after your doctor has pronounced you to be at maximum medical improvement.)