You will not be able to sue your grandmother for the money that she received on your behalf. Even though that money was meant for your support, no one monitors what that money is truly spent on and so it can be spent for the mortgage, rent, groceries, etc. You can go to the post office and have your mail forwarded to a new address or post office box. You can also notify SSI that you have relocated. I assume that your SSI checks ended at the age of 18, so you should no longer be receiving them. Where are your parents and how did your grandmother get custody?
Definitely notify SSI that you have a new address. If your aunt is withholding your mail, you can report her for mail theft:
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Family Court is a court of narrowly limited jurisdiction although sometimes it seems it creeps into our lives in all instances.
There is no petition you can file to "sue" your grandmother. You are not providing enough information as to whether she is your 'adoptive parent' via Article 10 proceeding for which she would be liable to you for support until you are 21 years of age. You do not tell us if she is your guardian although I gather that from your factual assertions. As a guardian, she is not obligated to pay you support as the government supports you with taxpayer funds.
However, having no duty to support you other than as perhaps your guardian, you could file a Guardian petition to vacate her order of guardianship. This would render an order you could take to your SSI administrator to shut off the flow of money to her. First, you have to check if there ever was a G-Petition filed in family court for her, and then use that file number to petition to vacate.
I cannot offer too many other suggestions as I do not know your case. Being 'kicked' out could be a ruse to give the appearance of emancipation but I am not certain so I cannot provide more information.