civician

Hi people, I was hoping for some second opinions on this issue I'm having with my baby. My 87 DX has been dieseling for a few months. About a month ago I was driving home from a job; after 2 miles the engine lost power and did a sort of shaking/dieseling. After a few seconds it would return to idle but when I pressed the gas pedal it lost power again. Initially this cycle would happen a few times until, the car would respond normally to pressing the gas and I was on the road again.

After a couple of weeks the car wouldn't right itself for a few minutes. A week later I would be sitting on the side of the road for maybe 5 minutes before I could restart. Now I'm scared to take it for a drive at all, noticing that the motor is sounding a little rougher when I start her up. 

I replaced the air filter and both fuel filters, as well as the battery because I was having issues with it as well. It didn't seem to help and now I'm thinking this is exhaust related? maybe my catalytic converter is clogged. My exhaust was in poor, rusty shape when I bought the car 3 years ago but the car always ran fine. 

Does it sound like the CAT to anyone else? What else should I check? A cheaper solution would be ideal; I don't have much extra cash and CATs appear to be about $150 (for mine, the type connected directly below the exhaust manifold) 

Can I clean the Catalytic Converter manually? Anyone have links to inexpensive exhaust components (if getting down there I would probably just replace everything, from the CAT to the tailpipe. 

Thank you for your help!