An antibiotic acts against certain bacteria. A cold is caused by viruses, so an antibiotic will not cure it or help you feel better. Yellow or green mucus, on its own, does not mean that an antibiotic is needed either.
Taking an antibiotic unnecessarily can still cause side effects, including diarrhoea or allergic reactions. Inappropriate use also contributes to antibiotic resistance: bacteria become resistant, making some infections harder to treat.
This does not make antibiotics any less important: they can be essential when an infection calls for them. Whether they are appropriate depends on a clinical assessment, not simply the name of a symptom. Different infections need different approaches, and even some bacterial infections can get better without antibiotics.