Some questions on sensitive topics to talk about.

Don’t beg, it is very very rare that would work.

Have you seen this program?

http://web.mit.edu/admissions/graduate/special.html

And yes, I agree with others that you’d be insane to turn down Caltech for MIT. At the very worst, you can transfer from Caltech to MIT and get an MIT degree, plus you’ll have the upper level classes at MIT which would be specific for your program.

BUT: you mention financial constraints - did you even look into how much it will cost you to attend college in the US? Travel to and from? Tuition, fees, room and board?

Do you even know if you could afford any of the colleges you were accepted to?