I am in the air force, being medically separted/board. However, I owe the air force $109,978. I would like to pay it back.

I wouldn't pay it lump sum, now that you are just starting out again.

You should be able to get a low-interest pay-back rate.

Go to the Judge Advocate and find out how you can pay it off
by the month. I suspect you are still employable as a physician, and
will be able to pay back on a monthly rate plus interest. Don't expect
to be forgiven any amount, and let the Advocate advise you.

Write your Congressman, and advise him/her and ask for advice.
Congressmen (state and federal) are sometimes the people who
can unstick things that get stuck, and they appreciate time to work
a problem. Many have excellent staff for this.