True allergy to alcohol itself is very rare. However, you may be allergic to other ingredients in alcoholic beverages, such as wheat, sulfite preservatives, etc. Some people are very sensitive to alcohol, but this doesn't mean they are allergic to it; they may have alcohol intolerance.
Many Asians experience unusual facial flushing after consuming even small amounts of alcohol. This is due to a genetic deficiency that prevents the body from fully metabolizing alcohol. Some studies suggest that people who experience alcohol flush have a higher risk of alcohol-related diseases, such as esophageal cancer and liver disease, if they drink alcohol. The only solution is to avoid alcohol.