This blog post contains anecdotal observations of my own, with some links tossed in. I hope it answers your question of, "Is Oatmeal Gluten Free?" Any brands I mention are because I've had experience with them. No money was paid to me to include them in this post. That said...
As someone who is allergic to wheat (allergy tested at the doctor and diagnosed well into my 30s), I struggled at first to find foods that I could eat without, ya know, hives and a belly ache. I had the blood test for celiac (negative) and decided to go gluten free to see if I could get rid of the belly ache and the itchies. Unfortunately for me, the only medicine that made my belly not ache so much contained blue food dye, also an allergy trigger! So you could see why I would jump on a diet change to see if it helped any.
I thought, at first, after doing research that oatmeal would be a slam dunk. Whoo-hoo! Something I could eat for breakfast, admittedly, one of the harder meals for me since I, despite being in my 30s, still loved kids' cereals like Lucky Charms.
But you know, I tried eating oats and still managed to get a slight belly ache and red dots on my wrist, which are a sure sign of exposure to wheat for me. I'm not saying I had a major reaction, but enough of one that my body was sending me warning signals to not eat whatever it was that I'd just eaten. Belly aches all the time can get pretty annoying.
Why was this? I did some more research and found that it could be because of crop rotation on the part of the farmers who grow oats. It could also have been shared equipment at the processing plant. I even read one article that said that some people's bodies just react to oats like their body would to gluten.
For me, though, I only buy myself certified gluten free oats to bake with, like Bob's Red Mill, since I can usually find that brand at stores I shop at for gluten free items. When I eat certified gluten free oats, I don't have GI issues or annoying itchy blotches on my wrists.
Certified gluten free oats are more expensive, but worth a try if you feel that you're still reacting to a non-certified gluten free oat product. I even dug up a coupon for you --- Bob's Red Mill has a coupon for $1 of product (and they sell non-gluten free things too). For those of you who might blend their own gluten free flour, the coupon should be able to be used on their potato starch, tapioca, etc.
Tip, if you ever get a deal on steel cut oats, you can use a food processor to break them up a bit more for baking. I've got a hand pulled food chopper that I have used before in a pinch.