It IS possible to be intolerant to wheat and still able to have other gluten, actually - "gluten" and "wheat" are not the same thing, not synonymous. 
I have a friend who was diagnosed as wheat intolerant, by an actual doctor, yes a real GP just one who was a bit more openminded than some of you. She is not coeliac, nor is she intolerant to all gluten - but she IS intolerant to wheat. She came off it completely for a bit and many niggling problems she'd had (acne, grumbly guts, persistent cough etc.) just disappeared. She was unfortunate in living very close to a bakery and one morning the smell of the fresh bread was too much for her, so after having been wheat-free for a few weeks, she bought a half-baguette and ate it all in one go. The reaction was pretty instant and enough to convince her not to do it again - her mucous membranes all swelled up, including her eyelids, lips, throat, nose, cheeks and face in general. She was off work for 3 days until it calmed down enough for her to function. Not an anaphylactic reaction, but scary enough - luckily her airways never closed up completely or she could have been in real trouble. I saw her 2 days after it, I went to see if she was ok - and she looked like she'd had her face slammed hard into a wall.
OP - start eye-rolling back at the ignorance of your "friends". At least there are two of you now to back each other up in terms of what you can and cannot eat; so if necessary, you can split the group and you two go off somewhere more appropriate for you - the other two can do whatever the fuck they like.
Also, see how you go with the oats - although the gluten component of oats (avenins) is fairly different from the gluten in wheat, barley and rye (all of which are very similar), some coeliacs still react to oats as well.