From the picture, I could not tell if the smoke was coming from inside the cat or the heat shield around the cat.
1. smoke is coming from AC drain that is leaking on cat
2. the weld on the cat is broken and exhaust is leaking out
3. head gasket leak and coolant is getting into the cylinders and inside the cat
As pointed out, codes are critical to figure out what is going on here otherwise we are shooting in the dark.
As above, this could simply be steam from the A/C draining onto the exhaust. However, the rough running may be a sign of a clogged catalytic converter, which gets hot, smokes, swells, and causes degradation of performance as a result.