Hi. Non-Muslim parent of college student (soon to be 2 college students) here.
First, please do not lie to your parents (or anyone, actually). Your personal integrity is more valuable than this.
Second, we are not wealthy at all. Our sons' school choices were largely based on scholarships. The oldest had choices, still, and had a full ride to pretty prestigious engineering school but chose a slightly lesser one because he is a musician and there are zero musical opportunities at the really good engineering school. The younger is currently choosing. He believes, like you, that it will make a huge difference in his ability to achieve his dreams (I'm semi-quoting him here). He has a full-ride to such a school, but it will be difficult logistically because it is literally 3/4 of the way across the U.S.
So, you might be thinking, "I wish my parents would give me a choice like that". Yet, finances preclude it for us because there are costs other than tuition, room, and board at all schools. We looked. Other kids' parents are taking out loans to send their kids (who had/have lower grades and test scores than ours) to Ivy League schools, and MIT. We are not taking out student loans. So, in a different way, I might look like just as big of a jerk as your parents.
I say all of this to lead to this: It isn't really that important. Of course, CMU would be ideal and, if you haven't applied, you need to ASAP. But, if you work hard to understand the material and concepts, you can become a Damned Fine Engineer just about anywhere that has an accredited engineering program.
'Not what you wanted to hear, I know. And you can write me off as just another parent backing up parents. We parents have fears - I wish my kids followed Jesus (yes, that one), as I do. But, they're not that impressed with him currently. Likewise, your parents probably want you to follow Muhammed. And your willingness to lie to them says you've probably already written that off. I suspect they know this and are hoping for some "influence" from a Muslim community. That's my guess.
'Hope this helps.