2006 Ford Crown Victoria P71 Transmission problem?

118,XXX miles

I'm in the process of selling my p71. I was driving it (in light rain) and the rpm gauge was acting up. I pulled off the highway to a side road and as I accelerate into the turn normally, the rpm needle shoots to about 3-4,000 Rpms and it will continue to climb and it doesn't change gears when it needs to. Once it hits maybe 5-6,000, the car bucks and the rpm's go back down to normal and it sounds like it changes gears. It sounds like it isn't going from 1st to 2nd gear. (I never dealt with slipping trans before so I'm not familiar.) it's happening all the time now. I checked the trans fluid 2 times and the fluid looks newish and there aren't any shavings. I don't hear gears grind. When it rpm's up to 3-4,000 like I said the car bucks and the needle goes down to its normal 2-3.000 and it's sounding like the gear sounds correct for that speed and what not. So it corrects itself to equal the rpm's is what it sounds like after the bucking motion. Like I said I never dealt with it before and I'm going to take it to a mechanic but I wanna know what we're dealing with first.attached is a video, I'm not revving it on purpose, it's doing that on its own with the slightest touch of the pedal.

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