Sorry to hear about your injury.
The short answer is "No," the other driver's insurance company will not agree to pay your future medical bills. This only happens when you are injured on the job and your employer is obligated to pay your medical bills, provided that a work comp doctor links up the injury to the proposed treatment. In your case, the other side's insurance company will settle, make a payment to you, but in exchange they will require that you sign a "release" which releases them, their insured etc. from all claims which you have from the beginning of time through the date you sign the release, including claims that may result from latent injuries you received in the wreck. In other words, in exchange for a check, they want finality. This is the reason you never should settle a case until you are very comfortable that you know the extent of your injuries.
In addition, depending on the amount of coverage that the at-fault driver had, you may have an underinsured motorist claim against your own carrier. If that is the case, it is very important that you immediately place your own carrier on notice of this car wreck and your continuing injuries.
Finally, you need to be aware that your health insurance carrier likely will seek reimbursement from you for the medical bills it has paid because of this wreck. This is called "subrogation" and if you fail to take this into account, it can have very negative consequenses for you.
If I can be any of assistance to you, please do not hesitate to call at 205-254-3927 or toll free at 888-295-7409.
