Please help - Hit and run, settlement, issues w/ insurance company

This is long, you were warned. :)

Background: I was involved in a hit and run while visiting NC in Jan 2020 (wherein my car was totaled and I suffered soft tissue injuries that I went to PT for several months for).

I took down the driver's plate info, but it took several days for the officer to provide the drivers insurance information. When I contacted his insurance company (GEICO), they informed me the driver had already opened a claim on his vehicle for hitting a deer. After he was questioned by the investigator for a couple days, I was told he admitted fault and I was then able to open a claim. Before I was able to open a claim, I was without a vehicle and stuck where I was, so I had to pay out of pocket for a hotel and rental car.

GEICO has already reimbursed me for the hotel and rental car. I am in the process of trying to settle with them for medical expenses, pain & suffering, and also pursue charges against the driver. I thought it odd that I never heard anything about appearing for a court date against the driver, so I reached out to the police officer who was on the scene that day. He told me that he was never informed that the driver admitted fault and that he is not able to pursue charges against the driver unless he has a letter from GEICO stating the driver admitted fault in order to present it to the magistrate. I informed GEICO that I wished to pursue charges against the driver and that the officer needed this letter to do so [and that it shouldn't be an issue given that their calls are recorded]. My requests for this letter went ignored for months until 12/1, when I was informed by a new adjuster via email that:

"I have taken this file over from the previous adjuster and will now be handling this claim. GEICO has made a fair offer for settlement of your bodily injury claim. Consideration was given for your incurred medical expenses related to treatment, pain and suffering based off any previous conversations and review of your medical records pertaining to your injuries and related treatment. Our current offer stands at $5,345.72. At this time nor in the future would we have this case valued in the range of your demand of $20,000.00.

"Liability is not in question for GEICO pertaining to this matter, your request for our driver's admittance is not something we are able to provide nor share as we do not have a recorded statement from the driver. In the event we did, it would be considered a work product of GEICO and unable to share without the related parties permission to do so."

I am at a loss for what to do. I do not feel the settlement offer is fair, and I also feel it is unfair that there have been zero repercussions for the drivers actions as he should be held accountable. I have already filed a claim with the insurance commissioner and am still waiting for an update on the claim. I have contacted other personal injury attorneys who've said, "..unfortunately we aren't able to take on this case, we recommend contacting the NC Bar Assoc. and requesting the appropriate attorney for this case."

I went on the NC Bar Assoc. website and requested free legal advice as I am in a low-income household and can't afford an can't really afford an attorney. I did get a response back, but it wasn't especially helpful. They responded with information I already knew, basically outlining compensatory and punitive damages and that both could be awarded in a civil suit. However, I would need to prove the other driver was at fault (hence a statement/letter from GEICO that the driver admitted fault which they are refusing to give me).

Also for reference, I've listed my expenses below, both what GEICO has already paid out and unpaid expenses: Paid (car being totaled, rental car, loss of use, and hotel) = $6,330.44 Unpaid (medical) = $2,835.72 I don't know how to calculate pain & suffering.

I just need someone with experience to be transparent with me. Does their settlement offer ($5,345.72) sound fair? What would be a fair amount for me to counter-offer given that they will not accept my offer ($20,000)? How is it possible that they cannot share an admission of fault from the driver? Who's responsibility is it to follow up or notify the Officer that the driver admitted fault? How do I go about pursuing charges and punitive damages against this driver if attorneys are not willing to help and GEICO is not willing to provide the drivers admission of fault? (Would that even be possible without the admission of fault) Should I just give up, accept their offer and move on?

Your time, help, and advice are greatly appreciated! Thank you!