After working with an Apple technician today, I have a solution for this issue. I'm not sure if it will fix every instance, but my iMessage on both my Mac and AppleWatch are now working perfectly once more.
1. Close out of all other programs, including iMessage.
2. Go to System Preferences > Date & Time.
3. Click the lock in order to make changes. Then uncheck "Set date and time automatically" before rechecking it.
4. I would restart your computer at this point and then reopen iMessage.
This is what fixed my issues and was told that there is something with the date and time that were interfering with the imessage server, keeping it stuck in time. My iMessage still shows as "Offline" but this has not affected any of my messages sending.