One more thing, (Columbo), check the exhaust pipes for transmission fluid leaking onto them (it). That could be causing the smell.
A brake caliper could be stuck, causing the transmission to work harder. Front end alignment may have suddenly gone bad due to a big pothole or tie rod end wear.
A car is just a lot of systems tied in together. One of those systems may cause trouble for another one of them. It could be just a transmission problem but things should be checked in addition to the one.