You are correct in that the TurboTax software will calculate the difference in what you paid to New York and what you would have paid to New Jersey, assuming your NY source income was earned in NJ. Per the State of New Jersey, your credit can't be more than the amount you would’ve paid if you earned the income in New Jersey (rather than New York).
Regarding your 1099, if that was NJ source income, it should not be subject to NY tax. Can you provide the income amounts you entered as well as the categories assigned to each income amount so that we can review your income allocations. In any follow-up post, do not include personally identifiable information.
As your office chair was purchased while you were no longer self-employed, then such purchase would not be deductible as a business expense.
@js1512
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