Before my tmj started I was clenching in the morning just before I was fully awake while I stretched and tossed about a bit in an effort to get up and turn off the alarm - but as soon as I was fully awake I would realize I had a headache and take 2 aspirins and it would ease up just before lunchtime although sometims it did linger all day long too. So yes, grinding or clenching can cause the morning headaches and wearing a night guard may help stop the grinding but some find it just gives them more to gnaw and grind on - but it will protect the teeth from the damaging affects of grinding and clenching. For some - grinding and clenching can be a learned habit or behavior in response to stress - although for the most part it may indicate an occlusion problem - but some have found changing their sleeping position, the use of a cervical pillow or sleeping less prone or with less pillows can often help as can biodfeedback and jaw and neck exercises at night before retiring. There are actually some sensor appliances that can be worn at night to wake one when they clench or grind to help break the habit or cycle as well.

Have you mentioned this to your dentist - it could be there is an issue with your bite on the one side - have you noticed any changes in the appearance of your teeth (rounded or very jagged edges, fractures or breakage, ridges) or tooth sensitivity, their position or feeling of mobility - these are sometimes signs of an occlusion problem. If you still have your wisdom teeth they could possibly be causing this as well.