I used to get this a lot after OW would update.
First, make sure you have a temperature program downloaded if you don't already. Sometimes an overheated GPU can cause this.
The second thing I would check, and it may sound weird, but check your recording device. Go into Sound, Recording, and make sure whatever mic you're using DOESN'T have the "allow application to take exclusive control of this device" checked. I know it sounds completely unrelated, but it's actual one of the known fixes. I've done that before and it stopped happening to me.
Thirdly, close the Blizzard app so it's not running in the background.