Sick, unproductive cough for 3 months, low grade fever bur normal chest xray i had history of asthma?

Likely asthma: Be treated for asthma to see if this helps your cough. Also think about pertussis, or the whooping cough. All the best, 3 months is a long time. See you doctor.

Uncontrolled asthma: could be very much your case, the fever could be due to intercurrent upper respiratory infection (eg sinusitis/pharyngitis/otitis), possibly viral, please check your physician/allergist if possible, good luck