I am eatting well and try to have enough rest but even a small amount of alcohol make me feel very sleepy and tired. What is the problem?

Sensitive to alcohol. Your body may simply not like alcohol, and be showing this to you. You could also be consuming other sedative-hypnotic or depressant medications, and in combination these build up -- making you sleepy. Or, you may have less of the enzymes needed to process alcohol in your system. Usually other symptoms would come along with this though, such as flushing and nasal congestion.