Which state would you consider moving to or do you have relatives at? If your mother is American, where do your grandparents live and could they help you with housing, voter registration…?
Moving at the end of January would have you join the 2nd semester of 11th grade. If you came with strong Dec SATs and could explain your curriculum so they know what is equivalent to Honors or APs it might be possible but it’s true moving in the 11th grade is indeed really hard.