1997 Honda Civic Speed Sensor problem?

1997 Honda Civic Automatic 106000 miles

Hi, I've been having a shifting problem for a while now, in conjunction with a seemingly broken speedometer. Speedometer needle flies all over the place while driving. Shifting problem only happens when I go from 2nd to 3rd gear. It's like a "whirring" feeling of the transmission trying to find itself (it doesn't make any strange noises). Once past that part, it runs really well. Been told by mechanic friend that the transmission and its fluid is fine. Also, speedometer was briefly fixed by Lucas Oil transmission fluid, but now it's back. Codes came back fine by the way. Friend thinking it's now the speed sensor. What do you think?