How can I transfer my mom closer to me?

I think the better plan would be for you to go to her. From what I read, this is very serious. I think it will be a long time before Mom can travel. Your profile says Moms 41? The hospital where she is I doubt will set up a transfer out of State especially clear across the country. You also have to consider health insurance, a lot do not go over state borders. Medicare does but very few suppliments.

As said Nursing School is not easy. All your energy should be going to your studies. You may want to put it on hold right now.

You might see if the nursing school will defer your admission by a quarter due to the family emergency.

If she can barely move, that private medical flight will cost thousands out of pocket

where are they or she going to live once moved from an area where they know people, have friends, know the neighborhood, know the stores?
Are you going to care for them/her while you are starting school? A very stressful program I might add.
To move them and all their belongings and to close up and sell the home they have been in is daunting.
for them if they can travel easily A flight would be the way to go. If mom needs help the airlines are great with that. If she needs more then you are talking either renting an RV and driving her or paying for Medical Transport. Both pretty expensive.
I get why you want them closer but I think you need to think this out a bit and play with the logistics.

I get why you’d want her closer to you, but this sounds like it would be a hard journey for your Mom.

And if you did move her to you, what’s the plan when she is recovered and out of the hospital?