A few thoughts:

Often anti-depressants take a while (up to a couple of months) to kick in fully.

If you decide that Prozac is not helping you then it is fine to discontinue. However, quitting cold-turkey is not a good plan - it is best to taper off slowly - your doctor should be able to advise you of a schedule for this.

Prozac is a member of the SSRI class of anti-depressants. I am not meaning to second-guess your doctor but trying one of the SNRI anti-depressants is something that you could discuss with him/her.