'94 Civic Transmission Shift

I recently bought a '94 Civic whcih is in great shape. I have a question on
the transmission. It seems to tach up quite too high when shifting from 2nd
to 3rd, and to a lesser extent (not as high) from 3rd to 4th. 1st to 2nd
seems OK. The manual says that it should tach higher when it is cold, and
indeed it gets a little better when warmed up. But it is still noticeable
then, and even passengers have commented on it. It's particulalry
noticeable when accelerating slowly. The shift itself is smooth, it just
seems to be late, and happens all the time, not intermittently. I don't
have a tach gauge. It has 68,000 miles and just had tuneup and trani fluid
change (though I don't think my mechanic flushed it and probably didn't use
Honda stuff). My last car was an '88 CRX, and the trani in it worked great
till I had to junk it at 188K miles due to rust.
I'm a newbie here. I checked some past posts for ideas, saw recommendations
to use the special Honda trani fluid, and mention of the shift cable and
trani control unit. It looks like my first step should be to get the Honda
fluid, and find someone to do a complete flush (I read that a fluid change
actually only replaces a percentage of the fluid because of what's in
hoses, etc.). Who does this kind of work?
If that doesn't help (which I suspect will be the case), maybe the shift
cable could be adjusted? Or have the control unit checked? Do I need to go
to a Honda or trani shop to do these? I don't want to spend an arm and leg
just to diagnosis and then get told it'll be hundreds to fix.
Thanks much
Greg