You have a hearing soon? News flash: It is really fucking serious. Employers are not going to set up some kind of group meeting when all they're going to do is give you a light slap across the back of the head and say "You're silly, aren't you?". There is more at play than a single issue here:
You smelt of booze. Number one, and the worst (assuming your job entails PR). As plenty of other posters have said, first impressions are critical.
You weren't showered/shaved/etc -> presentable for work. I've worked in a supermarket where if you showed up with a days growth, they'd force you to buy shaving gear and shave before you can start work. It is a fair assumption that when you go to work you don't cast ANY offensive odour, whether BO or booze or sex, that you're clean shaven and wearing the appropriate uniform.
You were late. Depending on the number of employees you have on a single shift, this can range between a serious problem, or no problem at all. My current job is one where I relieve a single person - I don't show, they can't leave; other jobs I've worked, they might not even notice until they check the sign-in system.
So, you've broken three potentially important BASIC RULES of employment. If that's a problem for you after you drink, then you don't drink. Simple. If you've been there for ages, and are a good employee, you'll be fine - they'll march you in to scare you. If you're new, or you're not a hard worker, or this isn't the first time you've made any of those three mistakes - you'll be out on your ass, and don't be surprised - they have a business to run.