At this point, the best thing you can do to strengthen your application would be a stellar SAT or ACT score.
Keep in mind that for international admits to top US colleges with fin aid, you have to be one of the top students in your country. It sounds as if you’re studying in Saudi while your parents work there? That is a bit more difficult to chance, since there are so many guest worker children studying there in multiple types of schools that are not the same as the schools for Saudi citizen children, and not the same as each other, so it’s difficult to show you’re one of the top students in your country (where you are also a guest worker’s child, not a citizen, but in Saudi that’s common). But a top SAT score, even if you can get it, doesn’t help as much as you might think, since there are plenty of US applicants with very high SAT scores who don’t get accepted to those universities that offer fin aid to internationals.
You’ve assembled a good EC record. You are a straight A student. Definitely study very hard for the SAT and get as high a score as you can. Beyond winning a major international competition, there’s not much more you can do, in your case.
You need a coherent back story for your essay, that would usually include, “I want to come learn what you have to teach me, and maybe go on for grad Ed in the US, but my ultimate goal is to return to my country and help my country utilizing my education in the US that you, US colleges, were so kind to gift to me.” But for medicine that doesn’t work, since in fact, there is medical ed available in most countries, it’s not really available for internationals in the US, and there is already a serious brain drain of foreign trained doctors who come to the US to practice (and earn far, far more money than they ever could have dreamed of earning at home). The US medical education system has no intention of training foreigners to become doctors in the US, especially if they need fin aid, and the colleges know that.
The public health angle could work, but the reality is that you have nothing from Egypt except citizenship and a passport. You have no connection there, you have no family there, no ties there, so it would be a stretch to make a compelling argument that you want to study public health (not medicine) in the US and then go back to Egypt to help your country, because, as you say, you really have no ties there. BTW, public health in the US is usually a masters level program, not undergrad, so the schools that offer aid to internationals might not be a match for public health.
Medical school in Egypt is a 7 yr program, and costs about 40K USD for the entire program (vs as much as 500K for private undergrad and med school tuition in the US), plus of course living expenses, which in the US would be about another 250K for 8 yrs, and much less in Egypt. The cost of the 7 yr program in Egypt should be manageable for a family earning 120K USD/yr in Saudi. You really should consider applying for this, as it is your most likely route to becoming an MD. Is there any way that you could complete the requirements, and sit the entrance exam? Maybe even plan to go do a last couple of years of high school there in order to fulfill their entrance requirements, and sit their entrance exams? Of course, it is extremely competitive to get into their 7 yr programs, and I suspect that acceptance is not always based upon merit, but upon connections and even bribes, but surely some Egyptians are able to get in based upon merit?
I think that with your public health summer program that you did, you could make a coherent back story for wanting to help your country (Egypt) by getting an undergrad degree in a helping field, with the avowed intention of getting a master’s in public health, and then returning to Egypt to work in public health, where it is very much needed. But the problem with manufactured back stories is that they don’t often ring true. Meanwhile, your true ultimate goal, which is to practice medicine in the US, is not likely to get you into a US college, even with your excellent record, even if you were able to get a perfect SAT score. Even if you are open about your intention to get an MD by attending a European med school (at full pay, of course), it puts the lie to your needing full fin aid for undergrad in the US, and just isn’t going to help you get into a US school. You see, so many US applicants say that they want to become doctors - the undergrad colleges just don’t want any more of those.