This is an interesting question, because it implies several things that need to be addressed. First, answering the question directly, the biggest problem with drinking alcohol when you are sick is that it will impair your ability to get over the original illness
by replacing good nutrition with calories derived from alcohol. You may also be impaired in other ways that cause you to behave in a fashion that makes getting over your illness more difficult. Additionally, drinking alcohol on an empty stomach, which often happens when people are sick and not eating normally, can also cause the alcohol to be absorbed more quickly, which can lead to other obvious problems. So while it is not necessarily "unsafe" to have a drink of alcohol, being drunk when you are sick is not a good idea and can be un-healthy (for other reasons as well). Ask your doctor
for more info.
Addressing all that your question implies, it is important to know if you are controlling the alcohol or if you feel that it is a vital part of who you are, and that you can not be separated from it. If you find that you think about cutting back, get annoyed at others who tell you to, feel guilty about your drinking, or need an eye opener, please talk to your doctor about your problem.