When you filed your own tax return did you indicate that you were a dependent on another taxpayer's return?
If so, then you consented to this.
However, if your cousin did not actually pay for more than half of your expenses and you earned more than the allowed amount then you both filed inaccurate returns and should amend your returns as soon as possible by filing Form 1040X.
This is not likely to get any Economic Impact Payment to you in the near future as they have already begun distributing them based on the information on file - but you should still file complete and accurate tax returns each year.
You may be allowed to claim the payment as a credit on your 2020 tax return filed in 2021, but there is not likely anything that can be done to correct the situation ahead of that.
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