Sent mail appearing in my inbox

The past couple of days, I have had (some, not all) sent emails appearing in my inbox when I have replied to emails that I have received. And the original emails to which I responded no longer appear in the inbox.

Now, before you jump on me, I have "Organize by Conversation" turned OFF, and the conversation does not appear in preview mode -- only the reply I sent with the email to which I displayed indented beneath the text of my reply.

It's driving me nuts, as this has never happened before, and I'm unable to file the original email I received in the folders I'd normally store it in the sidebar.

This does not happen with every email I reply to. I have not yet figured out a pattern.

This happens on both my office iMac and my iMac at home, so it's not isolated to one computer, and it seems unlikely that I would have inadvertently changed a preference on both computers within the same timeframe of the past couple of days.

I'm running OSX 10.11.5, Mac Mail Version 9.3 (3124) on a 27-inch late 2015 iMac, 32. GHz Intel Core i5 with 24GB of RAM.

I'm using a Gmail IMAP account. I have not yet determined whether my mac.com (iCloud) personal email is acting in the same way because I just don't have the same volume of personal email, and the situation has not presented itself, and I have personal mail coming into only my home iMac.

If anyone else is experiencing the same thing or has a fix, I sure would appreciate hearing about it. I have not yet tried deleting my account and starting with a fresh install of it because I haven't had the time.

Thanks!