Have you checked the in-game settings? Theres a "Hold to Speak" option or something thats been known to activate itself when people change console/platform. Happened to a couple of my pals.
Bring up your character menu, tab over to the right to "Settings", go down to Audio and check all those (assuming you havent already). Theres an option called "hold to speak" or something like that, if its on then turn it off.
Outside of that the only other thing I can think of is that the mic on your headset died (Turtle Beach are not as reliable as they used to be 😔) or your NAT type may be causing problems...