Ok, I gotta jump in here.
No fish do not get hiccups. If your fish is making a jerky hiccupy looking motion or looks like its trying to yack something up, it probably has hexamita.
Signs of hex are as you said 'hiccuping', loss of appetite or trying to eat but spitting it back out, weight loss, white pimple looking spots(not ick spots), or a general wasting away look.
If this happens to a fish in your tank, head for the paragon II quickly.
But if your fish looks like it is just yawning then its not hex. This is a lack of oxygen problem.
Need fish advice? Visit the Community Tank. A very friendly forum.
http://communitytank.aaquaria.com/phpBB2/index.php