I haven't heard of that and it didn't happen to me. If it gets worse ask your doctor. But maybe it's the prednisone or something, and if the azathioprine starts to work in a few weeks so you can taper off the pred, maybe the cough will stop.
19yr old female diagnosed with UC (pancolitis) in 2005 at age 15
125mg Azathioprine 1xday / 1 Mesalamine enema every night /
2000mg Fish Oil 1xday / 500mg Turmeric 3xday /
450mg Boswellia 1xday / 400IU Vitamin E 1xday
Arthritis in both knees
Also: asthma, acid reflux, and Reynaud's Syndrome