I have also suffered from anxiety most of my life and used alcohol as a medication.
I think what you're going through is normal. Early withdrawal after the acute phase is marked by various uncomfortable things...whether it's anxiety, depression, dizziness or feeling like your going to fall down. Panic attacks are also common and for me a few years ago coming off a HUGE drinking problem, those hit me really hard in the morning when waking.
I echo what others have said that it does get better in time, but it might not be a bad idea to explore with your doctor what options are best for you. For me getting on an SSRI (Lexapro) has helped my underlying anxiety tremendously. Early on I also needed a benzo as a rescue med, but I don't use it anymore.
Hang in there and check in with SR often!
