Yes, you would have to file 3 state tax returns.
You would report New York income on a non-resident New York state return. Which would include your New York only income.
https://www.nj.gov/treasury/taxation/njit23.shtml
Then New Jersey income on the New Jersey resident state return.
https://www.tax.ny.gov/pit/file/do_i_need_to_file.htm
South Carolina rental income on the non-resident South Carolina state return.
https://dor.sc.gov/tax/individual-income/faq
