Most coughs, colds, sore throats, sinus congestion, and cases of flu are caused by viruses. Antibiotics have no effect on viruses, so taking them for these illnesses will not make you feel better faster or stop you from being contagious.
What does help is rest, fluids, and time, plus symptom relief such as paracetamol or ibuprofen if appropriate for you. Most viral infections improve on their own within one to two weeks.
Taking antibiotics you do not need is not harmless: it can cause side effects like diarrhoea and thrush, and it contributes to antibiotic resistance. See a doctor if symptoms are severe, last longer than expected, or you have a high fever, difficulty breathing, or you are in a higher-risk group.