Hi in the 10s,
Not only Prozac, but nearly all of the similar, "SSRI" antidepressants, have been thought to occasionally lead to suicidal thinking in depressed individuals; this was most recently publicized in the treatment of adolescents. There is some controversy about this, in that its frequency is thought to be rather unusual, and that the rarity of this side effect warrants monitoring, but does not argue against the benefits of the use of these medications. Some think that the side effect of the SSRIs of feeling agitated, (known as "akathisia"), may lead to some suicidal thoughts in some.
The bottom line is that on one hand, no medication affecting the brain and one's mood should be taken without a doctor's careful monitoring, including for the rare occurence of suicidal thoughts as a side effect, depressed individuals can reap significant benefits from the SSRi anti-depressants, and should not have them withheld due to the fear of this rather unusual side effect.
If you depression is only mild to moderate, psychotherapy is as effective as medication, so you may want to consider this. Good luck!
-E. Seigle MD