If things don't improve in a day or two on the vertigo pills I'd definitely get to the doctor and demand further tests. I really don't want to frighten you but issues to do with balance can have other serious causes. It could also be the alcohol of course but if it persists and flares up at random like this I would advise you not to ignore it.
Either way I agree with the others, use this episode to fuel a re-think on your alcohol issues. Keep us posted.