You can call me Erica.
I was previously misdiagnosed with IBS and I was never able to eat greasy food without paying a price. I think untreated gluten intolerance exaserbates sensitivities to food in general. After going gluten-free (before I discovered additional sensitivities), I was actually able to handle greasy foods better than I could before, but unfortunately, I can't eat those foods now. If you're reacting to dairy at all, I'd consider that a sign of a food sensitivity. Casein, a protein in cow's milk, can often cause a latent reaction the way gluten does. I didn't think I was sensitive to dairy either. I would get a stomach ache and diarrhea right after having something like ice cream, but everything else was just random. I tried slowly eliminating it anyway since I knew it was probably a problem. Eventually I went a week or two without any dairy. Then I just happened to have some cheese on a sandwich without really thinking about it, and the next day I was in soooo much pain. I haven't had any dairy since.
You most likely have food sensitivities. I saw several doctors for several symptoms that I had, which were all caused by Celiac, but I never got a Celiac diagnosis because I tested negative and was never offered an endoscopy and I didn't know that was part of the diagnostic process until much later. If you want an official diagnosis, don't stop eating gluten before you're tested, otherwise you'll definitely test negative. However, even if you do test negative (like I did) and your endoscopy happens to be clean, I would recommend you try going gluten-free, regardless. It's easy to get a false negative.
Bleeding could be a sign of an anal fissure from strain on the tissue. I'm sure it's possible for Celiac to cause it, but it could also be a lot of other things. You should definitely see a doctor and make sure it's not something else like Crohn's, although Crohn's patients can also benefit from going gluten-free.