It would seem that Chekov's recovery was, in no small part, due to Terrell's death...after Terrell commits suicide, Chekov's eel somehow senses the death of its "brother" and thus instinctively forces its way out. And as soon as the eel leaves him, Chekov is able to recover relatively quickly.
(if the eel had remained in Chekov's head much longer, the "madness...and death" Khan spoke of, would have been much more likely.)
In any case, somebody must have seen to Chekov's needs, as he later reports for duty on the Enterprise ("Could you use another hand, Captain?").