Slow shifting between second and third gear with engine revving excessively

Car takes a while to shift between second and third gears. Car also revs excessively when changing gears. For instance, when I am on the highway I will accelerate to sixty mph and the car revs loud at 4,000 rpm. If I relieve pressure on the gas pedal and then immediately apply it again, it then shifts gears and the rpm's drop to normal. When I am slowing down from highway speeds it will jerk as its de-accelerating from third to second gear.

I realize this is likely transmission related. But I am hoping there could be an easier solution? Throttle body dirty? Spark plugs? Thanks