Is this bronchitis? should i go to the doctors?

Wounds like you have what is commonly called a chest cold. Most of these infections are viral and the usually last about 10 days, even though it takes weeks to completely get rid of the bug. If you have no fever, you probably don't have a pneumonia. You may have bronchitis just from all the coughing. If it feels like your chest is going to explode when you cough, it's probably bronchitis. Should you go to the doctor? I don't think you need to, but that is really up to you. People ask for antibiotics for respiratory infections all the time even though the cause is most commonly a virus. The doctor will most likely tell you to rest, take plenty of fluids, and use ibuprofen or acetaminophen for bodyaches. This will most likely resolve on it's own. Good luck.