Hello, and welcome to Just Answer.
I'm sorry your cat is experiencing this problem.
There are several possibilities for your cat to be staggering like she's drunk. If she has access to your garage and/or spends time outdoors, ingestion of highly toxic antifreeze can cause this type of drunken staggering and would require immediate vet treatment.
A condition called Vestibular Disease can also cause this symptom of staggering. It causes dizziness and sometimes can resolve on it's own, but other times may need treatment from the vet. Here is more information:
An ear infection can also be the cause of dizziness and adversely affect her equilibrium.
Hypoglycemia (low blood sugar) can also cause a staggering walk, in addition to other serious symptoms, so for the moment, you can rub some honey, karo corn syrup or maple syrup (pancake syrup) on her gums, just in case she is hypoglycemic.http://www.cat-world.com.au/hypoglycemia-in-cats
Cardiomyopathy, a heart condition in cats, can cause weakness in the hind legs, if a blood clot forms in the main artery carrying blood to the region. Feel her hind foot pads to see if they are cold or warm; if they are cold, there may be no blood reaching them.
Considering your cat's age and her current symptom, it would be advisable to have her evaluated in person by a vet, as soon as possible. If it is after hours for your regular vet now, bring her to an ER vet center for assessment and treatment.
I hope all will be well with your furry girl!
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