No, your tax home would be the general area where you work most of the time. It wouldn't have anything to do with where your bank is located or the address where you get your mail. The significance of that is you cannot deduct travel expenses unless you are away from your tax home.
It sounds like you are sharing home expenses with your sister, so your payments to her would not be rent income.
You can read this TurboTax article to learn more about a tax home.
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