It is possible you are going through gluten withdrawal. I did for three weeks - many do. I felt famished at all times (for the first time ever had to get up at night a few times to eat), got migraines and generally felt quite ill. Perhaps this is what you are going through.
My dietitian and a celiac specialist strongly recommend avoiding even certified GF oats for two YEARS after diagnosis. It is not a gluten thing but rather to give our guts time to heal. After my being strictly GF for nearly six months now I have just found out I am now also lactose intolerant. Grrrrr...I LOVE my cheese. But just to encourage you my tTG number went from 71.0 (waaaayyyy off the charts) down to 3.8 recently. Anything below 7.0 means "negative"!!!! Awesome news. So, it can be done.
In addition to oats I recommend eliminating dairly for the first two or three months if you can. I teach culinary classes so if you are looking for snack/meal ideas or recipes I would be happy to help.
Hope you feel better soon!