Not sure if it will affect Apple texts because that's outside the scope of my job, but I do know that iPhones and iMacs will run into issues if there are attachments above a certain size in the mailbox. If you've got a habit of texting pictures to people, and you have backups of the pictures, try deleting them from the message threads to see if that helps.
Really appreciate the response. I just went ahead and deleted the conversation with my friend, including attachments, to see if that helps.