Traveling to Egypt if one is HIV positive?

Whenever you travel with medicine, the preferred practice is to carry it in its original containers (and in your carry on, not checked luggage); bring only enough for your intended stay; and have with you a letter from your physician stating that the medication is required, is for your personal use, and what quantity you will be carrying. To protect your privacy, the diagnosis should not be included in your physician's note.

While your medications are not likely to be classified as controlled substances by the Egyptian Drug Authority, the Cairo International Airport does not refer to what are not allowed, althugh a recent article in Egypt Today does (and may not be comprehensive):

CAIRO –18 February 2018: Cairo International Airport released a list of the drugs, substances and medicines that must not be carried by passengers entering or leaving Egypt.

Sources inside the Cairo International Airport stated in press remarks on Saturday that the authorities are regularly distributing leaflets to passengers that contain the list of medicines and substances that passengers are not allowed to possess when leaving Egypt. This because there are many prescribed medicines that are allowed in Egypt but controlled in other countries.

For patients, doctor's prescription should accompany substances that are meant to be brought outside Egypt, the sources stated; adding that the prescribed prohibited drugs must be carried along with prior permission from a doctor and must not exceed 20 tablets. Possession of more than 20 tablets amounts of illegal drugs can be considered drug trafficking.

The list of the illegal drugs includes: Nicocodeine, Didrex Tablets, PROXEN, Mogadon, NITRAZEN, vaccine injections, KETAMINE INJ, Ergotamine, Dextromethorphan, Pulmolar, Co-Diovan, Kodinalin, Somanil, Phenobarbital, Nova Tablets that have an extended effect.

Valinil, Calmepam Tablets, neuril, Valium, Tranxene, LEXOTANI tablets, EN tablets, Xanax, CODASTIN, Codaphen N, somadril, Tussivan N, Korfas tablets, Migranil Tablets, Librax tab and Rivotril Tablets are also on the list.

TSE resources: Travelling with medicines

Edit (per @Doc comment):

Restriction categories relative to Egypt
Entry regulations
No HIV testing for tourist stays

HIV-specific entry and residence regulations for Egypt

An HIV test has to be performed at the Health Ministry’s central laboratory by everybody who applies for a residence or work permit (students, foreign employees, immigrants). Tests performed abroad are not recognised.

Foreigners diagnosed with HIV while in the country are expelled. The regulations are based on a Ministerial Decree.

HIV medication can be imported for personal use.

All foreigners planning to study and/or work (including training) in Egypt for longer than one month will be required to undergo HIV testing in Egypt. Information on this procedure will be provided by the Egyptian immigration authorities (Mugamma, Tharir Square, Cairo, Egypt) upon application.

Proof of yellow fever immunisation is required if arriving from an infected area. Evidence of an AIDS test is required for everyone staying over thirty days, for the purpose of studying or working in Egypt.