You should be just fine with the Dextron III fluid. Dextron II was the current tech fluid untill III came out in the mid 1990's. The III formula replaced the II and is backwards compatable as far as I understand. Since you cannot get Dextron II any more, III would be the fluid of choice.
After a total fluid change, it may take a bit to get the trans back to what it "felt" like before the change. You have fresh, thicker fluid in there, and that will act different than your old, worn out fluid.
Be sure to check your fluid level periodically over the next few days to be sure that no air pockets or voids gave you a false reading. Otherwise, just continue to enjoy your truck!