Hi. I had exactly the same problem, always waking up during the night and therefore not being alert during the day. I cured it by taking vitamin B supplements and making sure I got regular exercise.
Those with coeliac disease have an extra demand for the B vitamins (1). Whether we just don't utilise them well or just use a lot I don't know. If we don't get enough B vitamins we can get a bit anxious (well I do anyway). I have found that B complexes with B12 seem to more beneficial.
I recommend taking a vitamin B complex, consuming 100mg of vitamin B6 a day to start off with and then adjust as necessary.
all the best
(1) this is according to Adelle Davis, google her or search amazon for more information.