My mother isn't eligible for full Medicaid. What can I do?

Check the income limits for Georgia at dch.georgia.gov/eligibility-criteria-chart
I think you have the wrong information..

General Medicaid income limits do not apply to Medicaid Long Term Care Programs.
You need to meet with someone from either the Medicaid office or Aging Office to get the real scoop.
Good Luck

My dad lived in GA, his income was 2200$ a month, he had Dementia and previous strokes, after a fall he went to a Nursing Home.
He was eligible for Institutional MA, and received assistance after his Medicare days ended. He lived there 4 years. I am sure there is help for your Mom and you.
Let us know if you are not able to get answers and we will try to guide you in the right direction,

At $1200 a mo, she is within income limits for NH LTC Medicaid.

Have you actually gotten a list of documents required by Medicaid to establish your moms income & asset and had those reviewed by a NH or Medicaid caseworker? Has mom actually submitted a Medicaid application and been told she is ineligible? Income & Assets are evaluated differently for Medicaid but each must be within whatever your states Medicaid program has as its limits.

If yes and you have been told that mom is ineligible, then the problem is that mom is over the 2K in ASSETS allowed by Medicaid.

Income (like SS, pension) has a maximum amount & @ $1200 should be fine. So the problem is that somewhere mom has assets over 2k. You need to review all paperwork on anything that mom got a 1099 for (so produces a dividend and pops up on IRS/Medicaid matchup that there is an asset out there with value) or that is in moms name that is a non-exempt with a cash value (like a whole life insurance policy, or nonhomestead property, or savings) and so is taking her over the 2K asset limit.

The rules for individual NH LTC Medicaid are pretty straight forward: they have to be "at need" both medically and financially. For "at need" medically, it's that they need skilled nursing care. For financial. It basically means they are impoverished. If mom can't provide documentation on each, she will be ineligible till she can.