My DD2 had similar issues. When she woke at night she would be wriggling and seem like she had a sore belly. At around a year old I started pumping her full of yoghurt to improve the good bacteria in her gut. It seemed to work. Not that she became a perfect sleeper or anything (still wakes at nearly 2), but she did improve and didn't seem as uncomfortable when she woke.

But given you are coeliac, I would be following up on that.