From what I can tell, I think you have a great chance for positive results, assuming your essays and recommendations are good. Though it’s never wise to be overly confident for one’s chances at schools like Andover and Exeter, both of these are need-blind, so your need for substantial aid will not hurt your chances for either.
A general tip for applications and the like: stress accomplishments at various roles, not just your participation, even if in leadership. Did your travel soccer team finish high in a tough division, or win high-level tournaments? How about your debate and math teams? And how have you grown as a person through your involvement? Have you helped others in these groups raise their performances?
Specifically to Andover, they make a big deal about wanting “nice” kids. I think they would think very highly of your helping your siblings with remote classes. Though I wouldn’t make a huge deal of it, I think you should at least mention it so they are aware of it.