My iMessages aren't delivering but the other person can see them/iMessages sending as text messages.

Ever since yesterday my iMessages have either been sent as text message or not been delivered, but the person can still get the message and THEN they turn to text message. Its extremely frustrating and I'm getting really fed up. I'm running on a new iPhone 5s that I got only 2 weeks ago and running iOS 9. And before you ask, I've turned the phone on and off, restarted it, turned iMessage on and off, checked the Send & Receive, and this is happening on wifi AND data. And yes, all the people I'm texting have iMessage as well. Every now and then one message will send as an iMessage and actually be delivered then it just goes back to sending as text. I'm getting really annoyed and would loooveeee if someone could help me out.