There were no actual claims published that you person can not drink any alcohol while taking Amoxycillin or other antibiotics. Many people really believe that you should retain from alcohol while taking antibiotics. No one knows where this myth came from. It is so popular that it is sometimes even supported amongst some of the medical profession. There is only one group of commonly used antibiotics that may cause unpleasant adverse reaction when taken with alcohol. These are the imidazoles, of which metronidazole (Flagyl) is the commonest in use.
Anyway if you have taken Amoxicillin and plan to drink alcohol you should take into account some factors. The peak activity time of amoxicillin is about two hours and it is primarily metabolized by the liver. Alcohol is not absolutely contraindicated when taking amoxicillin the way it is with other antibiotics like Flagyl. Actually you can have a couple drinks only if you wait at least two hours after your dose. Please keep in mind that alcohol is also metabolized by the liver so try no to have more than a couple.
Alcohol is better taken in moderation because it could irritate stomach if taken with amoxicilin.