You will not get better any faster by takin antibiotics
Antibiotics have no effect on viruses. This means they will not help you get better any faster when you have a viral infection. Nor do they help you cough less or feel better.
Learn more about the diseases that can or cannot be cured by taking antibiotics
When you have an illness caused by bacteria, antibiotics will prevent those bacteria from proliferating any further. This allows your immune system to kill the bacteria. This means that it is not the antibiotics but your own body that cures you, by building up a natural resistance. This also means that you will not cure any faster of common bacterial infections by taking antibiotics.