If I was not at-fault for an accident in which my car was totaled, what can I do to get my car loan completely paid off and get reimbursed for the deductible?

Your property damage claim and separate personal injury claim (since you mentioned medical bills) should be filed with the at-fault party's insurance carrier.
You can reject the settlement offer on the property damage since it is inadequate to pay the remaining balance owed on the loan and does not include the deductible.  The deductible should be paid by the at-fault party's insurance.
If the property damage is not settled, you can file a lawsuit for negligence against the at-fault party.
It would be advisable to wait on filing that lawsuit because if your personal injury claim is not settled, that should also be included in the lawsuit for negligence against the at-fault party.
As for your personal injury claim, when you complete your medical treatment and are released by the doctor or are declared by the doctor to be permanent and stationary, which means having reached a point in your treatment where no further improvement is anticipated, obtain your medical bills, medical reports and documentation of any wage loss.
Compensation for the medical bills is straight reimbursement.  The medical reports will document the nature and extent of your injury and will be used to determine compensation for pain and suffering which is an amount in addition to the medical bills.  Compensation for wage loss is straight reimbursement.
If the case is settled with the at-fault party's insurance carrier, NO lawsuit is filed.  If you are dissatisfied with settlement offers from the at-fault party's insurance carrier, reject the settlement offers and file a lawsuit for negligence against the at-fault party.
If the case is NOT settled, your lawsuit for negligence against the at-fault party must be filed prior to the expiration of the applicable statute of limitations or you will lose your rights forever in the matter.
 

First, her insurance is HER insurance: it does not have an obligation to you. Rather, it's obligation is to protect her: to defend her in court and if she loses, pay the judgment against her, up to the policy limit; and/or to settle cases for her, if it thinks she'd lose if she tries to fight. So they do not have to voluntarily pay anyhing to you--they could choose to, if they think you'll sue and have a good case, but are not required to voluntarily pay. Rather, to get money from the at-fault driver and/or her insurer, you have to sue her.
Second, when property, like a car, is destroyed (totalled), the law only gives you the then-current fair market, or blue book, value--the value or worth of the property at the time it was destroyed. It does not take into account the cost to you to buy the property: if a car is worth $4k at the time it was destroyed, you'll get $4k (subject to your deductible, if you had insurance), whether you paid $10k cash for it, or financed it and still owe $3k, or were gifted the car and paid nothing for it. 
However, you can recover from the at-fault driver any portion of the fair market value, such as the deductible, not paid by your insurance, so you can sue her for the deductible. You could also sue her for any out-of-pocket medical costs you incur (e.g. any costs not paid by health insurance or Medicaid/Care).