I don't think the transmission service you did is the cause of your symptoms. It was about to happen anyway I expect. A proper transmission service can only help. The only thing that could possibly affect the transmission adversely is if the fluid change somehow stirred up some gunk which is now blocking some port or another. I guess that is possible. But unlikely, like I say, if the service was done correctly, probably just a coincidence.
Automatics are configured with 3 or 4 gadgets called "gear sets". Each gear set has two inputs, one for the clutches, and one for the drum. The one for the drum operates what is is called a "band". Each input to a gear set is a hydraulic fluid pressures, and are either on or off. Logically I mean. The pressure for a logic "on" might be between 10 and 15 psi, and for logic "off" might be between 2 and 8 psi, that's the idea anyway. So off/off might be neutral for that gearset, and on/on might be a 1.3:1 ratio, and on/off might be direct drive, a 1:1 ratio.
The pressure comes from a pump inside the transmission, the pump pressure tends to be proportional to the vehicle speed. So the transmission uses the pump pressure to decide -- this is done with a part called the valve body -- what each of the gear set's inputs should be. It also needs to be able to adjust its decision for what gear to use for engine load, so there's a method inside the transmission to do that, either with a vacuum modulator (as on my Ford truck) or a throttle position modulator (common to GM I think) , or on most modern vehicles there's computer involvement, often using electrical solenoid valves.
So something wrong with all that. First thing I'd do is ask a shop to measure the pump pressure. And go from there. You may indeed need a rebuild, but it could also be just a bad solenoid.
One idea, if you feel lucky, do the transmission service a couple more times. You might want to purchase the fluid at a Chevy dealership so you can make sure it meets the required specs. Replace the filter each time. And sieve the contents of the bottom of the pan & old fluid you drain out for signs of metal debris. You can only get about 30% of the fluid out each drain and fill. So maybe just doing it a few more times will fix the problem, knock on wood. Best of luck.