indeed, the 1st unit is the catalytis converter, it is located there in order to heat up quickly so that it can be effective.
only thing i find strange is why you have one located there. my car has simple headers and the catalytic converter is located UNDER the car.
still, you'll need to have it opened, cleaned out and resealed. it can also be replaced with a simple pipe since this unit is only wide because it needs to increase its surface area to make it more efficient. personally i believe in having the unit opened and cleaned out rather than replacing it with a length of pipe which will not seal correctly andd will eventially fail due to rust.
from what you have described to me it seems your cat is choked quite heavily and your car is struggling to breath, hopefully once this is fixed your problem will be solved.