Hi
@samochod, from reading and not as professional advice or opinion:
looking up webmd.com - Prozac side-effects by likelihood and severity - taste problems are listed an infrequent side effect but also this medication can cause a low level of sodium in the blood. Some persons with low sodium in the blood perversely avoid salt.
There are other conditions which affect sodium levels and can be associated with symptoms of depression (mayo clinic.org- Hypothroidism).
Before I was prescribed anti-Ds in the past I was tested for low thyroid and low Vitamin B12, as these. i was informed, can mimic depression.
I would suggest asking your doctor about the above: sodium levels and thyroid function as part of his/her assessment.
Again these are just suggestions.
Best wishes with a resolution to your troubles.