I have been recovering from a nasty bout of illness, asthma, flu, cough, etc but now I have developed a constant ache in my right arm. Concern?

Not sure why? Having constant ach in r arm should not be as result of any of those problems, if continue i will check it out with your doctor. Good luck thanks.
Cough. Get a chest xray, an ache in the arm could be reffered pain from a pulmonary process like pneumonia--or maybe just a pulled muscle--but i'd reccomend a chest xray.