What is anoxic brain injury? Is it enough to determine the patient has it by just having an eeg

Usually. Physicians rely on a history, physical examination, a period of observation of the patient and changes in their examination, eeg, and ct of brain and/or MRI of brain to make this diagnosis. I'm sorry you and your loved one are going through this.
Anoxia. Anoxic brain injury is a diffuse, severe, irreversible injury to the brain typically with loss of the distinction between grey and white matter on imaging. It is usually seen on imaging in conjunction with an anoxic event in the history. Eeg can show evidence of severe brain injury but can't in general tell you the cause.