auto trans won't shift up

I have a 91 Buick Skylark, auto trans, 2.5liter. It starts just fine. Takes off immediately into first gear. Also has reverse. But, it won't shift into 2nd gear or higher. Anyone seen this problem before, or have any suggestions. I been through several repair manuals in the last few months, but can't put my finger on exact cause.

Not enough info. But I'll give you my 2 cents on what I'm thinking.
First, Change you transmission filter and gasket. If you do it yourself, it should cost you about $15.00. Replace the fluid in the pan. ( depending on the Trans, about 3 to 4 quarts, maybe a little more. A service center will charge you appox. $70.00 - $120.00 for them to " Service the Transmission."
Then, go to a Service Center ( Pep Boys, a Dealer, GoodYear...) Get a transmission flush. It pushes out all the old fluid and puts in New stuff. This takes about 1 hour for the service center to do. Cost, about $69.00 - $100.00.
While changing your filter notice the color of the oil. Is it Pink, or is it dark?
Like I said first, Not enought info to really know what is going on. But, this is the cheapest way to check it out Yourself. If you never changed a Transmission filter, Don't worry, it is not Rocket Science or Brain Surgery. Just take your time. Loosen all the bolts then take down one side let the oil drain out, then the other. If you never done anything like this before and you take your time, count on 1 hour.