Can a recent bout of bad coughing from bronchitis dislodge a gallstone and block the pancreatic duct?

Likely unrelated: Yes, you can have a gallstone leave the gallbladder, enter the bile duct & cause biliary obstruction or pancreatitis. But coughing would be unrelated & not be expected to dislodge a gallstone & cause it to enter into the bile duct.

Unlikely but possibl: Gall stones dislodge to biliary ducts due to normal physiological pressure built up in the gall bladder contractions , how ever known to get acute attacks after car accidents etc , cough is unlikely cause.