My daughter has a cough and is irritable, can I have antibiotics?

Hello, my daughter is 2 and a half years old, she had two colds in the last month, since 4-5 days she does not run from her nose but has a very big cough, since 2 days she is very irritated, she sleeps very badly and does not eat much, she made 2 ear infections in the last year and they are the same symptoms, she told me that her ear hurts tonight... My daughter expresses herself very well so I know that she is in pain