I am unconvinced that going gluten-free caused a hypo episode, except as a temporary coping mechanism for your body to get through the transition.
Here's one possibility for your hyper symptoms. Assuming your gluten-containing foods caused inflammation to your thyroid, then the removal of this inflammation could lift your thyroid function. It might slowly be recuperating, starting to produce more hormone. If all other needs are met, then T4 is properly converted to T3, and T3 can get into your cells. During times of feeling hypo, T3 is apparently "stuck" in your blood temporarily. Then if conditions improve -- stress is removed, you eat a good meal, you're not tired -- the T3 moves into the cells and ramps up your metabolism.
My husband has been struggling with this as he learns to support his adrenals. To get a better handle on what's happening, he takes his temp at 3, 6, and 9 hours after getting up in the morning. When his temp stays in the 97's one day, but gets into the 98's the next day, he can be counted on to get temps later that day approaching 99. Plus his thyroid feels tight, his head is throbby, and he sleeps very lightly. This appears to be caused by T3 moving into the cells and the excess being cleared out of the blood. But then his system calms back down.
I hope you haven't gone into Hashi's, as it sounds like a miserable condition. You might consider taking serial temps to give yourself more feedback. As far as I know, going hyper involves increased temps and faster heartrate.