Will a bad transmission make my car go into limp mode

(Automatic transmission) recently I just changed the
cylinder head and I start the car and everything works
fine. Now when I put it in drive it revs up to 3000 rpms and
the car wants to bearly move till it gets up to like 20
mph... now if I drop it in D2 it takes off perfectly and I have
to manually shift it till I get to drive.. but after I drive for 15
minutes my car loses all acceleration and I can't go no
higher the 15 mph.... now after I sit there for 20 minutes
my car will crank up perfect and drive home untill it does it
again.... can someone please help me I'm fixing to change
the transmission and I want to know if that's the cause of
my car loses acceleration or what????