Current research (in contrast to some older studies) suggests that birth control pills and even changes in natural hormones over the menstrual cycle have very little to no effect on alcohol metabolism.
Different people having different responses to drinking alcohol can be due genetic variations in two enzymes, alcohol dehydrogenase (ADH) and aldehyde dehydrogenase (ALDH). A fast ADH enzyme or a slow ALDH enzyme can cause toxic acetaldehyde to build up in the body, creating dangerous and unpleasant effects. These variations may affect a person’s risk for alcoholism, though there are many other factors.
You probably have enzyme variants that give you more unpleasant effects than ‘average’. You don’t need to get your liver enzymes tested unless you drink heavily.
Stay on the birth control pills and stay safe. A lot of the harmful effects of alcohol are not diseases like liver cirrhosis or pancreatitis but social – the man who drinks and perpetrates domestic violence, the person who should have taken a cab but thought they were OK to drive. There is no shame in being a light drinker, but if you’re with friends who aren’t please look out for them.