1995 Saturn SL2 Automatic Trans problem

I bought a 1995 Saturn SL2 (1.9 liter, 4 cyl) from a local dealership about a month ago. They told me they purchased it from a Saturn dealership (it was a trade-in for a new Saturn) and that it was in perfect working condition. My husband and I checked the car out, checked all the fluids, everything looked great and all the fluids were fine, no leaks of any kind (still).

Right away I noticed there was a transmission problem. Every car I have ever owned has had some kind of transmission problem, I swear sometimes I am cursed!

The problems: I don't know if this is common but when I am braking, the RPM's hop up to over 2k RPM's for just a second, this usually happens when I've braked below 20 MPH. The other problem is that sometimes when I am driving the car, it appears as if it gets "stuck" in a gear and it won't accelerate or switch gears, the RPM's go up very high and it takes a few moments for it to go to the correct gear. There are no grinding sounds when this happens, my last car (1985 Olds Delta 88 lt. Ed) had a horrible grinding noise and shaking when it was driven. It sounds nothing like that, but it does sound as if the transmission is being taxed pretty badly when it gets stuck like that. Once I have slowed down and re-accelerated, the car is fine. It doesn't happen THAT frequently, but it does happen when I've been driving the car for a long period of time (45 minutes or more).

I was told by a friend that knows a little about cars that is sounds as if my transmission is slipping. Is this the case? I have not taken my car to a mechanic yet because I am afraid of the news!

Thanks in advance for the help.