Well, It depends on the Location,Whereabouts in zamalek you want it.
and If you get a nile view or not, cause it's much more expensive.
I think you're being a bit overcharged though.
The exchange rate between the Dollar and EG Pound is 1:5.5
so I think a Reasonable price for a 3 bedroom would be around 9000 EGP, Almost 1700 USD.but i'm not really sure, cause the rents keep going up every year or whenever there is a price hike.
My advice for you is to seek some egyptian friend of yours and ask him/her to contact the agents for you, that way you'll get to know for sure if you're being overcharged or not.
If I were there, I would have really loved to help you.
you can get any work colleague to do it for you.