Not a physician but when I've been prescribed antibs for a similar problem as the OP's poor fish, I've been told to take the full dose for the correct time even if I'm feeling better. The logic is that stopping earlier allows any surviving bugs to develop a resistance to that particular antib – and voila, a superbug is born. So the problem may or may not be taking them for months (that may be a problem, idk) but it incorrect dosing for too short a time is also a serious problem.

Also, how do you know the Dr doesn't tune the dose unless you've seen what they give to every other patient?