1992 Toyota Celica RPMs jumping and car not shifting

In my 92 toyota celica, sometimes when I first start it, the rpms jump to around 3000. And it idles around 2000, which seems too high.

Then, while driving, it shifts fine into 2nd around 35mph at aprox 3000 rpm. But after that, I can get my speed up, but it doesn't shift, the rpms just keep climbing. I can get it to about 80 and it still wont shift and the rpms are sitting at 4500. What could cause this? And also, will running the car at 4000 rpm hurt the motor?