You definitely need to contact an attorney in the county where your husband is jailed for assistance. The attorney may or may not be able to help with the jail situation, but he should be able to get something done on the child-support contempt, which appears to be the reason why your husband has been incarcerated. It is not unusual for a noncustodial parent to be put in jail for nonpayment of child support. Courts will differ in their opinion as to what is an appropriate amount of money (legally, it's called a "purge") that it might take for the parent to be released from custody. If he was put in jail for nonpayment, then there should be an order stating what he needs to do to get out of jail.
A local attorney should be able to help you with getting a copy of the court order under which he was locked up, and that attorney also may be able to help with the jail situation. You need to get a good criminal defense lawyer who might have some contacts in the local sheriffs department that can help with that.
Nothing contained herein shall be considered or construed as creating an attorney client relationship between the party asking the question and the attorney. All legal problems are different. The answer given is only a general response based upon the facts provided and should not be considered specific advice for your case. Always contact a lawyer for advice about your particular circumstances and issues.
Unfortunately for your husband, the fact that he cannot work now does not "excuse" the child support that he should have paid prior to notifying the court of his inability to work. Thus, the only thing he can do about his arrears is pay them (somehow).
That being said, I agree with Mr. Canale that there may be some way of releasing him from jail relatively soon. He should definitely contact a local family law attorney for assistance with this issue. (Actually, I guess you would need to contact someone on his behalf.) If he cannot afford an attorney, you can contact the Georgia Legal Services Program, State Bar of GA Pro Bono Program, or your county's bar association to see if he qualifies for legal assistance.
Your husband may also have a valid claim against the jail for their failure to provide medical care. You or he would need to contact a different attorney to address this issue (possibly either a Personal Injury attorney or one that practices Medical Malpractice).
~ Kem Eyo
The above answer is a general explanation of legal rights and procedures. It does not constitute legal advice. Nor does it establish an attorney-client relationship between the individual posting the question and the attorney providing the answer.