Yes, flaxseed is gluten-free. If you do have celiac disease, you have a lot to learn but it's a little easier nowadays with new US food labeling laws and lots of good substitute products available.
I was dx 5 years ago with celiac and just last month with Crohn's. My Crohn's is fortunately moderate without a lot of complications at the moment. They also say I have some IBS going, which is probably true. My GI said to ditch all the specific food advice about Crohn's and figure out what works for me. But from what I've seen so far, much of it is the same already.
Let us know how your test results come out. If you do have celiac, I can recommend a great forum that promotes 100% gluten-free compliance and some resources for you. The GI also said is it very rare to have both diseases. I hope you fare better than I am with your results!
Dx with Crohn's Aug 2007; celiac sprue July 2002; Type II diabetes Nov 2006. Current meds: Entocort, Asacol, Levoxyl, Fosomax, various vitamin supplements.