I was beginning to have the same problem with my 98 auto. Depending on when and where I was, but mostly it would not shift out of first until high RPMs when I left work. It would also feel like it had a bald spot, or delayed gear engagement when finally getting around to going into second gear. This is probably due in part to my not letting the car warm up as usual as I wanted to ge the Hell out of there! I had 50K miles on the car at the time.
I doubt that my tranny was ever serviced as I bought the car with 9K miles on it, and I never took it in for tranny work. That will be happening tomorrow (flush, fill, and tranny cooler install).
Anyway, you most likely have a problem with either the clutches and/or bands. You may as well pick up a TransGo shift kit for street/strip use. Take the car into a tranny shop and have them modify the bands and install a few extra clutch plates to help durability iussues. Read up on TCOAA's Jerry's Mod to get an idea of how far you want to go. As far as the TransGo kit goes, consider using the stiffer 1st to 2nd gear shift if you want performance, or the not-so-stiff shift if you want confort instead.
Shortly after, or at the same time, either install yourself, or have installed the B&M Super Cool transmission cooler. Get it off of Summit Racing for less than $60 delivered. Get the one that is aprroximatley 7"X11"X3/4".
Let us know how it goes.