Your situation is pretty straight forward: you are either
A US citizen
A US Permanent Resident Green Card holder
An person here on a visa (which would make you an international students as far as admissions/financial aid)
A an undocumented student (if you over stayed your visa)
It sounds to me like you are in the US legally, but you are waiting for family to apply for an receive their green cards. While you are undocumented, you are still considered an international student as far as admissions and financial aid.
This means at most schools, your ability to pay will be a factor in admissions.
Since you have been in the US since your were in kindergarten, is it safe to say that you your whole high school career has been in NYS? If yes, then you will be eligible for instate tuition at SUNY if you graduate from high school.
While you are eligible for in-state tuition, the process is not need blind to you, meaning that your ability to pay will be a factor in admissions. Because of your status, you are not eligible to file the FAFSA for federal aid and you will nt be eligible for TAP. You can however file the paper FAFSA for consideration for aid (it will most likely not happen at SUNY since the state legislature just voted down financial aid benefits for undocumented students who have DACA).