2009 Pontiac G6 Issues: Where Do I Start?

Whenever I turn the car on, I have no Check Engine light or any indicators
showing something is wrong.  It idles fine as well.  But after I put it in gear
the problems begin.  My RPM red lines when I'm idling.  I won't even have
my foot on the gas and it sounds like I'm flooring it.  My temp gauge also
red lines like my car's going to overheat after about two minutes of me
putting it in gear and driving around.  It will red line, stay there like it's
overheating, but then it goes back down to 0 and starts all over again.  After
I drive for a while, even just up the street, the RPMs still red line after I put
the car in park.  When I turn it off after that, it sounds like the engine's still
trying to stop running for a minute before it stops making noise.  Does
anyone have any ideas as to why it might be doing this?  It wasn't doing all
this when I bought it and I didn't know if this is a common problem with G6s
or why it's doing this now.  I also wanted to know if this sounds like
something I can repair on my own, like a fuse or something, or if this is
something that professionals will definitely have to handle.  Please provide
any help you can.
Excelsior.