Will a bad transmission solenoid cause my bonneville to not shift correctly?

What is your question?

I have a 01’ Pontiac bonneville & I can feel when it switches from gear one, but from there my RPM only rises. I can only go about 50mph because I am nervous it will overheat the engine. Is it one of my solenoids ???

What makes this problem better or worse?

Slowing down makes it better in a way but RPM still kinda high

How long has your 2001 Pontiac Bonneville had this problem?

About 2 weeks