You should not drink, and you definitely should not get drunk, when you are sick. There are a few different reasons for this. First, if you are sick, you may have a fever
or otherwise be disposed to becoming dehydrating. Alcohol is also very dehydrating, so you risk becoming quite dehydrated from the combination of the illness and the alcohol.
Second, as part of treating your sore throat
or cold you may be taking other medications, such as over the counter medications, that could interact with the alcohol. In particular, taking anti inflammatory medications like tylenol or ibuprofen while drinking is not a good idea, as the interactions could cause damage to the stomach or to the liver.
If you think you may have strep throat, then you should get in to see your doctor
right away rather than trying to fix this yourself at home. If it is in fact strep throat, it will require antibiotics to go away. Your doctor can perform an examination and decide whether strep throat is likely; they may also do some simple tests to confirm the diagnosis, such as a throat swab or a throat culture.
In the meantime, drink plenty of fluids, rest, and stay away from alcohol.