During a coughing spell this morning I experienced a sudden sharp deep in my left buttocks could I have herniated a disk?

Possible. Besides disk buttock muscle ligament tear, injury etc are possibilities. Check with your md.
Possibly. Such a pain could be radicular in nature, that is, the pinching of a nerve exiting from the spinal cord. Coughing is known to increase interverterbal disk pressure. If the pain worsens or travels further down the leg, i would see a physician to get evaluated and get a referral to physical therapy to strengthen your core muscles by doing plank exercises, among others, to stabilize your back.