Check the kickdown switch (under the accelerator pedal) to make sure it isn't stuck or shorted, and check control linkage at the fuel distributor. If the linkage (or cable, I don't know off the top of my head which on the 560) is disconnected, the tranny will "think" you are holding the accelerator all the way down and won't upshift.
If the linkage and switchs are all working, yes, refusal to upshift is indeed and indication of a seriously sick tranny. Sorry.
1972 220D ?? miles
1988 300E 200,012
1987 300D Turbo killed 9/25/07, 275,000 miles
1985 Volvo 740 GLE Turobodiesel 218,000
1972 280 SE 4.5 165, 000 - It runs!