Another connection question - Cairo
 

Hope I can get an answer here as it has been decades since I've traveled internationally and some of what I've read does not line up with my past recollections. And perhaps it's the countries I've visited.
These flights are on one itinerary with Travelosity.

Flying JetBlue to JFK then Egypt Air to Cairo (T3) and connecting in T3 to Hurghada.
When I land in Cairo, will I have to go through immigration or will that occur in my final destination - Hurghada? Depending on this answer I wonder if my bag must be picked up and rechecked in Cairo.
I would have thought I'd clear at Cairo, but signs I've seen in pictures show connections are in one direction and immigration is in a different direction.

Any info appreciated.