Messages marked as read even though threads were never opened

I purchased my phone about a month ago, and have been having this problem since then. I didn't think it was a problem until around two weeks ago when I woke up and went into my messages app and saw read threads (ones without the blue dot next to them) I never opened a single thread because I was still sleeping when I checked the times the messages came through.

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I had one instance where I had a few unread text messages while I was texting my friend. After going back to all my threads, all the unread text messages were already marked as read.

Just today, my phone was locked and I received a text notification. I unlocked my phone, it went to the home screen, so I went to my messages, and that thread was already marked as read (no blue dot next to it). This has never happened to any of my previous iPhones, either.

Also had the same problem from two weeks ago happen again this morning. When I woke up today, I usually look at my notifications to see if someone texted me while I was still sleeping. I didn't have any text message notifications. That's when I checked my messages (no new messages or the red bubbles indicating new ones) and had about 5 different people who texted me - all read, all different times, and multiple messages.

At first I thought it was the notification bar or the thumbprint unlock, but now I'm not quite sure what it is. This instances probably happen more than the times listed, but these are the times I particularly remember (mostly because I had to reply by a certain time and missed it because I never got the text notification!)

Has anyone had a similar situation? Should I get a new phone?

Thanks in advance!

Phone: iPhone 6s Plus, iOS 9.3.2

What I have done:
Turned on and off read receipts
Restarted my phone
Changed the different types of message notifications
Turned off second reminder of text message
Turned off the landscape side view
Searched online for any related issues (nothing came up)