Do I owe US tax on the interest from my NRE and NRO accounts in India?

Yes. As a US tax resident, you're taxed on worldwide income, so interest from NRE, NRO, and FCNR accounts is all reportable and taxable on your US return — even NRE interest that India treats as tax-free. India does not withhold tax on NRE interest, so there's nothing to credit; you'll simply add it to your US taxable income. NRO interest, by contrast, has Indian TDS withheld (often 30% before treaty relief), and you can generally claim a foreign tax credit on Form 1116 to avoid double taxation. You also must disclose these accounts on an FBAR (FinCEN 114) if your foreign balances exceed $10,000 total, and possibly Form 8938. Keep year-end statements and interest certificates from your Indian bank so you can report accurately and claim the credit.