My cough started off as a wet cough and now it went to a dry cough. Wheezing when I breath. Chest pain. And shortness of breath.

Probably a URI. Probably a virus. But if it continues, you should consider an atypical pneumonia or pneumonitis which requires a z pal.
Work up and Mgt. Your illness most likely is due to a virus, associated with airway inflammation and reactivity which led to wheezing. Your shortness of breath and chest pain could be due to asthma triggered by the illness, and needs to be evaluated. Most bacterial lung infections do not worsen asthma, but some do, and your physician can order lung function tests and antibiotics if needed.