Engine Revs Up

I was driving down the interstate on the drive down was perfectly fine my car preformed amazingly as it had been the whole four months that I have owned it. I drove at about 80 mph for an hour and a half no problems, when I got to the town I stopped for a little while at the gas station (just to get something to drink then left town again.) Halfway home, about forty five minutes later the engine revving as I was doing 80 mph in sixth gear and would rev from 3000 rpm's to 5000 rpm's all of a sudden and then drop down again just as quickly, I did not notice it at first over the music in the car. Then when I noticed it it started doing it for longer and longer. I dislike revving the engine anything over 4000 rpm's just in case and so I let my foot off the gas and it would drop normally, but when I put my foot back on the gas it would jump right back up to 5000 rpm's, but no higher at 80 mph. My first thought (incorrectly) was that the clutch might be causing the problem somehow so I let off the gas and pumped the clutch a couple times and went off again and it seemed to fix the problem for about ten minutes. When it started acting up again I could see the faintest trace of white smoke coming from under the hood so I pulled over and stopped to raise the hood. No smoke that I could see until I went under the car and could just barely see some down there. When I put my hand underneath the car right below the oil pan it seemed a little hot, but I thought that it was because the car was running. I could not see anything wrong with it so I decided to get back in and start back home. When I put it in gear and pressed on the gas the engine revved up really high as I slowly rolled back. I called my father to come pick it up and he took a look at it, he could move the shifter into any gear without having to use the clutch at all even when the car was on and he was trying to move and it just started rolling back, he could move it into any gear without needing the clutch. He thinks it might be the linkage in the transmission or something like that. I was hoping someone would know for sure that way I could research how much it would cost, like I said I purchased the car four months ago and so I am still paying it off. Thanks to anyone who can help.