Not too sure about Prozac, I have taken it in the past but not as a starting treatment, I was on Citalopram then switched to Prozac.
Unless someone else knows I would expect it will take several weeks or more to feel the effects like other SSRI meds.
They can work very well however for panic and anxiety and as long as you can rough out any initial side effects and maybe feel a bit more anxious for a few weeks you should do well and get your old un-frazzled brain back
Steve