Hard Shifting

Hey guys I have a question.I have a 97 Galant with the 2.4L in it and I was wondering if it is normal for this car to shift at high rpm's.What I mean is when I'm driving down the road it will shift into 2,3,and 4th gears at around 3000 rpm's.And I feel every gear and there's no smooth transition into the higher gears.Is this normal or am I looking at a possible transmission problem?The car has 203 thousand miles on it with the original engine and transmission.I don't know if the transmission fluid or filter has been replaced before I bought the car but I do know I haven't done that yet.Allot of people say not to change these because it flushes out the crud that is acually helping to keep a good gear ratio.But if my tranny is slipping then I don't see I have anything to lose from doing this.

Could there be something else causing this problem like a bad module or something else?I had a friend hook it up to one of those high end OBD scanners that the professionals have and the car isn't throwing any codes for anything and appears to be in perfect working condition.The only thing I see to be wrong with the car is a short in the harness for the after-market radio that I haven't gotten around to fixing yet and I have noticed the rpm gauge will go up higher than the car accelarates.i will hit the gas pedal and the rpm's will go from 1500 to 2000 rpms but the car doesnt pick up speed.I have to push the pedal more then it picks up speed.I know there is probably allot of things that can cause this problem but I'd like to know where to start looking first.