Sounds like there is a text block on your line or that its provisioned incorrectly. iMessage uses the data network, which is why they are working. Call 800-922-0204 from a different phone into customer service for them to troubleshoot. This is a peer to peer forum and we cannot see your account. Let me know if this helps.
You also should be able to log in to your on-line MyVerizon account and see if that line has a text block on it