I would look into an integrative physician to make sure you're not missing underlying physical issues. In my personal experience mainstream peds do not run enough, or the right, tests.
I love a book by Kenneth Bock, MD called "Healing the New Childhood Epidemics . . . " I would check my library for it, as well as alternative treatments for anxiety.
My biggest concern with Prozac was (if I remember correctly) that there is a rat study out there that shows stunted growth. A neuro-psychiatrist reassured me that she hadn't encountered that problem in her practice - but this was a gal who was 4'10 probably and I'm not sure she'd ever acknowledge anyone else as "short."
If my child were 7 looking at Prozac I would be very concerned. I would ask the prescribing physician about all the possible side effects, including stunted growth (i.e., whether, indeed, that is a possibility - no matter how small).
Anxiety is very, very tough to handle. My heart goes out to you and I hope that you can get good solutions for your child.
I am not a health care provider of any type - this is just my "mom" opinion.
PS: I just noticed that it's your ped who wants to prescribe. Before doing that I would go to a pediatric neuro-psychiatrist for another opinion.