Bringing your mobile phone to Egypt is a good idea but go to your local mobile phone store at home and check that your phone is unblocked for roaming in Egypt.
You can also get your cell phone unblocked before your leave home to take an Egyptian SIM card which you can buy for around 10LE and the top up cards are from 10LE to 100LE.
I think buying an Egyptian SIM card is the best way to go because it allows you to phone taxis, your hotel/accommodation etc. etc. and gives you independence.
You should always ask the hotel or place you are staying to take note of your mobile number in case they need to contact you. If you didn’t show up for a day or two or were late for a tour or appointment you made through them it would be nicer if they could call your mobile phone prior to alerting the police that you might be missing! Also should your family call for you the hotel could pass on your Egyptian mobile number to them if you had forgotten to give your family that number. I know, as a Mom I freak out when my kids (now grown up adults) go away on holiday and I can’t contact them!