Ambien is a sedative in a class of drugs known as "hypnotics." It is not a benzodiazepine. Withdrawal symptoms typically do not last for more than a few days.
There's no way to be certain, but unless you've been taking any other drugs, like the benzos you mentioned, then alcohol withdrawal seems a likely candidate for your symptoms. As to how long your anxiety will last, there's just no way to tell. If your anxiety preceded your most recent level of drinking, then the primary disorder may be anxiety, rather than either insomnia or an alcohol use disorder, or a consequence of putting down the drink.
If you want more certainty, then you need to consult your doctor. Either way, it's probably a good idea to meet with your doc.