I have a writ of garnishment against me in Fulton County, Ga. Consequently, my creditor froze my personal bank accounts. I am self-employed and I am a member of an LLC which has business accounts. Those business accounts were opened in the name of the business under a separate Federal tax ID number but I am the sole signatory. I am concerned that my business accounts may be subject to freezing to satisfy this debt. Are business bank accounts subject to seizure to satisfy personal debts?

Not normally unless the debt is related in any way to the business, if the LLC is done properly. ( and not federal or state tax liens)

But that does not mean they will not freeze the accounts, and you have to prove they are business accounts.

But you have to be sure you do not pay any personal bills from that account, you don't pay your cable TV for the house, you do't pay the house payment and so on, It has to be business only. Once you start paying personal bills from it, it is then a personal account again.