95 Century transmission problem (?)

Hey, this is my first time posting here and I want to thank y'all for the forum.

Here's my problem:

I was driving my car on Tuesday up to Atlanta when I started to have trouble. I pressed the accelerator and the car sounded like it was 'reving up' and didn't 'catch' to finally go forward. It did this in reverse and in drive and the car has automatic transmission. I got the car to a hotel parking lot and called a tow truck to take it to a mechanic.

Before I got it to the mechanic, I noticed that my muffler was hanging a bit from the car on one side, another driver was telling me flames were shooting out from underneath the car, and I was low on oil.

When I got it to the mechanic, I was informed of the minor repairs made (basically, filing up holes in some lines, I don't exactly remember) and the guy said that 'it was a transmission problem, it's about to go' and recommended some places to take it too. I have my suspicions about it being a transmission problem because if it were, then I don't think the car would still be able to drive. I don't know a terrible lot about cars, so I'm probably wrong.

I wanted to ask the people on this forum, based on the situation, their thoughts. Also, what actions can I do (such as motor oil, carbonator cleaner, etc.) to make the car run better.

Thank you for your help/advice.

The smoke/flames were probably oil burning on the hot exhaust pipe. You're lucky. Make sure that mechanic fixed whatever was leaking. Look for oil drips and fresh oil where you park.
The transmission sounds like its slipping. It could be low on transmission fluid. You can check this yourself - the dipstick is towards the rear of the engine. But it needs to be warmed up and running in park when you check it. If thats OK how long has it been since you had the transmission serviced (fluid and filter changed) You need to do that around every 30,000 miles. A clogged filter can cause slipping. That's a relatively cheap thing to try. Find a reputable transmission repair shop for the service. But there's always a chance its more serious. If the service doesn't do it, then you're probably looking at more expensive repairs. If the shop where you had it serviced was reputable, you might have them do the repair too and maybe they would credit the service on the repair bill.
Good luck.

Sounds like you may have been dripping tranny fluid, not oil. this car has external tranny lines to the cooler, but no external oil lines. Low tranny fluid would cause the symptoms you describe. I would just keep an eye on the fluid levels and no further repairs should be needed. Good Luck.