<p>I agree with the suggestion that you apply to top schools such as Harvard, MIT, Princeton, Stanford, Yale, because you will qualify for need-based aid at all of them and they are quite generous. as is Rice. I do believe that you are competitive for all of them (it does not mean that you will get into all of them, but that you have a good chance). Look into schools that are in the Questbridge program as well.
Your EC's are fine, don't worry about them. Taking care of your siblings IS an EC.
One factor to consider is convenience of travel to and from Houston. When applying, asking for application fee waivers so that the fees do not impose and extra burden on your family .</p>
<p>Good luck!</p>