my iphone shows "sent as text message"
The "sent as text message" means your text message was sent using SMS, not iMessage. Because the message wasn't sent through iMessage, neither you or the person you are texting to have access to read receipts, which allow you to see whether or not the person you sent the text message to read your message.

This often happens if you're in an area with bad signal, with no access to wifi, 3G, or LTE coverage and the message can only be sent via SMS.