Transmission only drives 35 miles per hour,stays in second gear.

I will need to know the transmission we are talking about. Here is a site that will help you identify your thttp://www.nastyz28.com/chevy-transmission-identification.phpransmission.
I would say it is the shift solenoid, but we must know which applys, please let me know.

Check transmission fluid level could be low.if transmission fluid look dark brown smell burned need fluid filter change.if all ready done problem could faulty tps sensor or stick first and second shift valves.down shift cable worn out adjustment or the VSS SENSOR FAULTY.

Check your Transmission Fluid level first, make sure it is at the full mark.

If the problem persists, you either have debris that has clogged the flow of fluid, or your transmission has started to fail. When a transmission is starting to fail, a few gears can still work. If this is the case, you need it rebuilt/repaired or replaced.

Sorry for the bad news. Cross your fingers that you only have low fluid.