It's a predominantly Muslim area. A head scarf, whether partial or total, would go a long way towards gaining you the respect of those you travel with and among -- better if it covers all the hair, ears, and neck as well. Trousers or skirts should cover the full leg, to the ankle or to the top of the shoe/sandal. Shirts should not expose the chest below the collarbone, or the arm above the wrist. All attire should be loose so that it doesn't showcase your curves. Makeup should be left at home, because that's frequently assumed to belong only to prostitutes. Sandals are fine. Basically, show only your face, hands, and feet. Otherwise, you may be mistaken for a prostitute, and they don't treat those very well over there.
As a bonus, this modest attire will also keep you from sunburn. Also, the looseness of the clothing you should wear will keep the air flowing nicely around you, so that you don't get a sweat rash from the rubbing of tight fabrics against your skin. Take along sunscreen anyway, though, because your face, hands, and feet will need it.
According to Maimonides and to Rav Yoseif Karo (Joseph Caro), a Jew is permitted to enter a mosque by Jewish law and even to pray there, but according to Muslim law, no non-Muslim is permitted inside. Stay respectfully outdoors and enjoy the scenery, unless you really must use the bathroom; if so, at least stay out of the worship spaces and the wudu room (ritual washing).
Do not say you're Canadian (even though it's Eddie Izzard's advice, which is usually quite good). Socially it may not make much of a difference, but if you say it in earshot of anyone who has a right to demand your passport, and you're proven a liar, it could be seen as an attempt at fraud or espionage, and it won't go well with you.
Check what sort of wall outlets are in Egypt and Jordan, and buy adaptors so you can recharge your cameras, rental cellphones, and other electronic devices.
Friday is the Muslim holy day. Wear your best clothing on Friday to honor your host country, and on Shabbat to honor your Judaism (in training). If someone wishes you salaam aleykum, wish them "wa-aleykum es-salaam." That is, wah-ah-LAY-koom es-sah-LAHM, and it means "upon you, peace." Practice until you sound fluent in that phrase, at least.
If you hear someone shouting "Yallah!" it means "by Allah," and is also shorthand for "hurry UP, for the love of G*D!" so either put some speed on, or step out of the way.
Always carry your passport, other identification, and a little money in a pouch around your neck, and a little more money in a hidden pocket of your clothing. Best, keep it
under your clothing, and only pull out a little at a time while in your hotel room or in a bathroom to make it more accessible.
Read
this and other sites concerning travel tips for women, and also make sure your other family members read similar material. Not only you and your mother, but also your father and brother, should know the special perils for women in certain areas of the world.
Show obvious respect for your parents. Do as they say, don't make faces, better yet call them sir and ma'am, offer to help them and do things for them in public. Not only is that what the Torah and Talmud suggest for children (of any age, as long as one's parents are living), but showing any level of disrespect for them is a sure path to losing any respect you may have gotten from your host country. Respect for parents is HUGE over there, and we could learn a thing or three from them.