I would not be worried about taking it. It is unlikely it will make you weird thoughts worse. Just be very open and have an escape plan to call for help mif your mind goes off the reservation.

I would just wonder why the doctors are suggesting such an outdated drug when a newer drug may be able to give you a better result.

One of the side effects of Prozac is anxiety. You need to be less anxious. Did they consider this need?

But anyway, once you start taking it, welcome to the world of nausea due to SSRI's. The nausea will become less as time goes on.

fyi, It sounds like you saw a psychiatrist who also suggested getting the Prozac prescription started. Psychologists as you mentioned in your next to last paragraph do not normally have the ability to prescribe medicines.

It helps to understand what each specialist can do for you.