Call Geico and file a claim for your mother. Geico should explain (what) coverage your mother bought, that will be the job of an adjuster.
If mom only has liability, then they can do nothing for her vehicle damages. Sounds like mom did not buy UMPD (Uninsured Motorist Property Damage), thus can't do anything for her vehicle also.
But, mom (might) have medical payment coverage that would pay for her medical bills up to the limits she bought, then her health insurance (if she has any) would take over and pay the remaining medical bills.
Your mom (might) have UMBI (Uninsured motorist Bodily Injury) which would pay a settlement for her injury when she is done treating, if in fact the drunk was uninsured.
You (imply) this accident happened very recently, so are you sure there is no insurance with the drunk driver? If the police came to the scene and the drunk was arrested for being drunk, then the police would have asked for proof of insurance, or can run the plate through the DMV to verify the owner of the vehicle, which would show the name of the insurance company and policy number.
Insurance follows the car (not) the driver, thus you need to verify or not if in fact that the car was insured or not? You can call the name of the insurance on the police report and file a claim on their policy. If in fact the drunk was uninsured, then they would be required to send you a denial letter in writing to you. There could be a "possibility" that the vehicle was insured, and if so, then they would pay to fix your mothers car or if totaled, then pay for the actual cash value of the car.
So, get advice from Geico 1st, then also file a claim on the policy that the DMV has on record of the insurance that the drunk had when he/she registered the car when they renewed it. Some times, people buy insurance for 1 month to register their car, then stop paying, thus the policy lapsed.
If in fact the drunk is uninsured, then find out if co-workers or friends can help out driving you till you can figure things out.
You need to sort things out, which means taking care of your mother, and you may have to drop your school classes and your free internship, since you can always go back to school and may need to find a full time job, till things can get worked out and maybe buy a used car with your job. If you can't pay rent, then what does your school classes do, since you may not have a place to live or your mother.
After my divorce when my daughter was age 6, I worked full time and went to school full time, since I only had 1 income vs 2 when married, thus you have to make choices to survive.
You might want to talk to a lawyer for legal advice.
retired auto claim adjuster