Have you checked the level, the color, and the smell of the transmission fluid?
When was the last time that the transmission fluid and filter were changed?
When was the last time that the spark plugs, air filter, and fuel filter were changed?
I would strongly suggest that you get this car to an independent transmission shop (NOT AAMCO, Lee Myles, Cottman, or any other chain operation) for an evaluation. It sounds to me like you have transmission problems and possibly it is also in need of engine maintenance.
And, just to prepare yourself for some possibilities–if you are told that it needs a new/overhauled transmission, start thinking about whether you want to sink perhaps $3,000 into this 15 year old car. You may conclude that it is better to just buy another car if the news is particularly bad.