We have a visa sticky here, but basically yes you will need a visa and you can just buy it at sharm on arrival, your reps will direct you to the right desk. Then you dont need to worry about it anymore and have it for whichever day you decide to go to Cairo.
http://www.holidaytruths.co.uk/viewtopic.php?f=32&t=189&p=1351680#p1351680
I think someone is pulling your leg about being whipped in the streets for not covering your elbows.
In Sharm more or less any type of normal holiday clothing appropriate for your age will go. It's a man made resort and they rely on western tourism to make a living. You aren't supposed to go topless round the pool or on the beach but some do.
In Cairo I would suggest wearing something long and loose to keep you cool, although I would imagine many just wear longish shorts and T shirts. If you go into religious buildings it's respectful to cover your head and your shoulders and not have your boobs hanging about the place, but you can just take a scarf or pashmina with you in your bag.
As for being 'whipped in the streets' ?
![:que](/storage/forum/smilies/vque.gif)
Not sure where that has come from, someone scaremongering no doubt.