The rpm guage flickers up and down along with the water guauge

I have a 2008 grand prix, when driving it sometimes feels like ( when the car is on cruise control and it hits the speed it's gears down.) It feels like that when driving and the rpm guage flickers up and down along with the water guauge. Water guage goes all the way down when the car accelerates. Please any info will help. I'm a single female and afraid to take to shop without getting an idea of what it could be.

Thanks in advance