All messages will only show the latest message received, but not the rest of the conversation until I send a response

I'm having some issues with my messages, text and iMessage. When I receive a message it will only show the last one sent from that person, even if they have sent me multiple texts. I am then not able to see the rest of the conversation until I send a response back. Even then the message takes longer to send than when messages is working properly. I've tried resetting and restarting the phone and it is still doing the same thing. It has done this in the past and restarting the phone usually worked, but I recently did the latest software update and it is now doing this consistently. Anyone have any similar issues or ideas to maybe try and fix it?