I would not think too much about you drinking 3 beers. If you decide that you want to stop drinking then don't drink. After 3 hours you should be legally allow to drive with 0 BAC in your system.
Just because you crave a cold beer does not mean your alcohol, if that was true then everyone would be a foodaholic. Knowing your sign of over drinking is also important just because you over do it alone but don't do it in public does not mean your alcoholic. You could just have a problem with alcohol when your alone with your thoughts which is always a bad thing to do in general for an alcoholic or a non-alcoholic person.
Anyway good luck with not drinking. Watch out for your triggers!