My 2003 Silverado at times will show rpm but not mph and will not shift gears.

overdrive is the fourth gear.D1,D2,D3,D4 now drive truck at 80 kmh
cruise at steady speed no fuel pedal movement, downshift from D4 to D3 you should feel RPM raise .. after push brake pedal a little you should see RPM raise 300 to 400 rpm.
shift pattern is 1st gear ,second gear,3rd gear and lock up(torque converter clutch). 4th gear with lock up
hope it helps

there is a computer that controls your rpm gauge, your speedo, and your shift. check that and your speed sensor. the sensor is faster and easier.

Dirty Shift Solenoids

Have to Google your trans unit or model
& see what the inside looks like, as far as
shift control items go

It may not be going into converter lock-up
either,that is some high rpm that will overheat it
also & ruin it for good

sounds a little like a cruise control problem.
they used to have a centering adjustment that kept the speed within a range. If the range somehow shifted to the high end this would cause your surge. it would be a screwdriver slot on the outside of the case.cw increase ccw decrease. yours is set too high or cw.
I work the screw back and forth several times in case dirt entered the cruise module.

If it is not going into overdrive or lockup it could be the fluid or an electrical problem. Some of the shifting is controlled by solenoids now.
You may have to get a transmission shop to evaluate it for you.

Have you ever had the transmission fluid and filter replaced, do that and see if that cures the problem.

check your tranny fluid and filter. you may have a clog some where or could be low on tranny fluid.

Sounds to me like transmission issue might want to have this check.............

That is normal,If you do the same speed in 4th gear the rpm's will almost double.

The rpm's will repond faster in a manual than an automatic.

In a manual the engine supplies the power required directly to the gear that you have selected thus the engine rpm's will increase or decrease as needed.

Yes you need to have it adjusted.