Prozac is a SSRI antidepressant and should not be stopped abruptly because stopping it abruptly can result in discontinuation / withdrawal symptoms like dizziness, insomnia, tingling sensation in body, lethargy etc to name a few.
Patients who are taking 20 mg of Prozac can taper it down by start taking 20 mg every alternate days for 3 to 5 days followed by start taking 20 mg after every 2 nd day for next 3-5 days and then can discontinue it.
this slow tapering can help in avoiding discontinuation symptoms however please note that the rate of tapering may vary from patient to patient and can be slower or faster depending on the tolerance power.
you can discuss about this strategy with your new doctor and hopefully you will be able to taper it down easily.
[ Please feel free to discuss further if you have any doubt / query in your mind ]