EtteBette is right ~ trust your doctor, give the prozac a chance, it may take time for it to begin working. Not all ssri's (one type of antidepressant/family that includes paxil, prozac, zoloft, effexor, etc.) make you in to a zombie.
Prozac is not a new medication. I know several people that are on it for years now with very good results! Just know that it may take 3-6 weeks to see an effect, and maybe even an increase in the dosage. Many people take 20 m.g.