Do I need to take medication for bronchitis?

I have had a cough for about a month, dry, sometimes bringing up coloured phlemgh. So went to the doctor's today, and she listened to me breathe, and said I had bronchitis. She prescribed me some antibiotics, and an inhaler. Now, the anti biotics were covered by my health plan, but the inhaler wasnt, and would cost 120$. Got the antibiotics, didnt get the inhaler. Can I get better just taking the antibiotics? Ive only got like 5 days worth, doubt I could get another prescription, and dont want to have to pay 120$ for a puffer for what I see as a minor ailment. Thanks