iMessages sends messages as iMessage and text

My iPhone 6 is sending my messages as both an iMessage and a text (SMS) message. When I send a message to another iPhone, it appears blue (as an iMessage would) but the majority of the time, it doesn't say the message is delivered (about once every twenty messages, it will say a message was delivered). However, whoever I'm sending the message to says they receive it as an iMessage, regardless of the fact that it said the message was not delivered. A few minutes after sending the message, the message will be sent again as a text (green) and the recipient will again receive the message as an SMS. I've tried restarting my phone, logging in and out of iMessages and Facetime, but nothing works. When I send messages from my computer, everything works fine and the messages sent are only iMessages (it says they are delivered, and they are not sent again as an SMS). Please help so I can send iMessages again! It's incredibly frustrating and I want it to be fixed.