Every time I drink a little alcohol, even just one beer, I get very bad headaches. The next day I am dizzy as well. What may be the cause of this?

Any meds? Are you taking any medicines? Alcohol can interact with a lot of meds and make you feel badly.
Adverse reaction. Some people have an adverse reaction to specific chemical substances, and alcohol is no different. You most likely are simply experiencing an adverse reaction to the alcohol. Unfortunately, you should listen to your body, and avoid alcohol to avoid these side effects. Best wishes.
Alcohol sensitivity. A deficiency in the enzyme alcohol dehydrogenase will will make alcohol poison for you. Don't drink it.
The alcohol. For some reason it does not agree with your body's makeup so i would avoid alcohol if i were you.