u cant balance the oxygen because u havent figured out the dissociation of ammonia. let me make it clear:
NH3 + H2O --> NH4OH (altho its supposed to be aq. NH3, since in reality ammonium hydroxide does not exist. but it doesnt matter since u'll learn such stuff later.)
so, dont split up NH4+ and OH- !!! i hope its a mistake on your part
now try balancing the equation.
your modification is slightly correct. put the cation in front and the anion behind and u get NH4I, ammonium iodide. sounds right doesnt it?