When I first start out it‘s ok, then I hear it shift ok- it must be shifting into 2nd, I go faster and it tries to shift again and has a problem- I hear a humming noise for maybe 2 or 3 seconds, then it finally shifts. I have a 1999 Ford Escort with over 200,000 miles on it. I added transmission fluid and it checks ok. I have never changed the transmission fluid on my car-because it is expensive. Some people say, if I change the transmission fluid, that will fix it. I hope I don‘t have to buy another transmission.
I'd guess you need either a new modulator valve, or a simple linkage adjustment.