1990 525i automatic transmission feels like it's slipping

When I start out from a stop, it accelerates great until about 5-8 miles per hour. Then it feels like it's trying to go to another gear and can't quite
get there. If I accelerate during that time, the engine RPM goes up but there is no more accelerate in speed.
The car has about 230K mile but I had the tranny replaced with a use done and I think the tranny had about 100K miles on it.
Also, as I go from 35 - 45 mph, it changes to higher gears twice, in just 10 MPH ?!
Any ideas?
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