Can a refugee living in a camp get into Harvard?

NO ONE applies just to Harvard. A normal list for an international student needing aid would include 15-20 universities.
Also, odds are that Harvard is your dream because you heard of it … but are you able to differentiate it from Princeton? Northeastern? Williams? MIT?
Just because you dreamed of something as a child doesn’t mean it’s the path for an adult.

A big issue: if you enrolled in credit-granting courses toward a university degree then you’re no longer eligible for financial aid at most places. What degree is that online university preparing you for? Is it regionally accredited? Are you taking MOOCs or classes with proctored exams?