Basically you are asking if you can emancipate from your parents. In practical terms, that means you are saying that yoiu can proivde your ow home, food and utitlities. Not many 16 year olds can get a job that would pay those expenses, particularly if they also go to school. So, in those practical terms, it is possible but rarely a good idea.
If your mother is too ill to take care of the cleaning and ordinary household chores, maybe your father should look into assistance in the home so that you can balance chores with ordinary teen life.
This answer does not create an attorney-client relationship. It is advisable to consult with an attorney with full disclosure of relevant facts for a comprehensive leagl opinion.
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