If the RPMs suddenly shoot up to a much higher level, but the speed of the car does not increase, then it is fairly apparent that you have a transmission problem.
One possibility is that the transmission is downshifting to a lower gear–probably second gear.
The other possibility is that there is excessive slippage in the transmission.
I strongly suggest that you get the car to an independent transmission shop (NOT to a chain place like AAMCO, Lee Myles, Cottman, Mr. Transmission, etc.) for assessment.
I am assuming that your Rav has automatic transmission. If it is a manual shift car, then it sounds like you have a slipping clutch. Either way, this needs to be rectified before you wind up stranded.