OS X Mavericks :: Mail Being Sent Is Not Using Correct Email Account

I am running OSX Mavericks and using Mac Mail. I have several email accounts set up including 2 different gmail accounts. My preferences are set up so that new messages are supposed to send from my primary gmail account. However, over the past couple of days, when I reply to a previous message or create a new message the message appears to be sending from my primary gmail account. That's the address that shows up in the box showing from which account the message is being created. The message uses the signature that is set up for my primary gmail account, and the message appears in the primary gmail account's Sent mail folder. However, when I look at the actual message that was sent (I tested this by sending it to another non-gmail account of mine), the From email address showing up is my secondary gmail account. So, replies are coming back to that secondary account, not the account from which I sent it. 

I do not have this problem when sending messages from my iPhone or iPad, so I'm pretty sure it's strictly a Mac Mail problem. 

I've checked the Preferences to ensure that my Composing settings have it set up to send from my primary gmail account, and it is set up that way. When composing the message, everything indicates that it will be sent from the primary gmail account, but instead it goes out as if coming from my secondary gmail account. 

This is definitely a new problem. I've not updated anything on the Mac OS recently. The only updates that have been applied recently are a Flash Player update and an MS Office update. This problem started before either of those were applied, I believe. I know for sure it happened before the Office update.