Muffler glowing red...

My LeSabre 91 has another boo-boo. After about 5 minutes of engine running my front part of the muffler gets hot (glowing red). It is a wider part (exhaust pipe?) which is located between driver and passanger seat under the floor (of course). When it is hot it makes clicking nose. When you drive it even makes car shake some. I have a felling that it is a problem with exhaust sensor or something like that but I am not sure... Heeeeeeeeealp!

Something is making a LOT of backpressure in the muffler. A baffle had probably brokem its weld, and is stopping up the system.

Get a new muffler, the backpressure will hurt the engine in the long run.

Well, I just found out that my V6 engine is working on only 4 cylinders. Top coil of 3 coil pack is dead. I think that explains why my car was shaking and Catalytic converter was glowing hot. i will try to replace the coil pack and I will let you know if it took care of all the problems.
Thanks again,
Alex
P.S. Does anyone know how to trouble shoot Speedometer?

Hello again,
Here is an update. I went back to the salvage yard and replaced an ingnition console for another one. This one finally worked (all 6 cylinders!). Turns out this was my problem all along (see my previous thread). After I wiggled some wires even my speedometer began to work!
I would like to thank all of you who was real help to me. I will keep my eye on this forum and may be I can be help to others too.
God bless,
Alex