I also strongly recommend getting a celiac test. Here is some info:
For most people, the serum anti-tissue transglutaminase (tTG-IgA) is the best antibody blood test for screening for celiac disease; however, it is important to also get a total serum IgA. Having this total serum test will help bolster the reliability of the tTG test. The reason for this is that while the tTG test is very reliable, its reliability is dependent on the premise that the person being tested adequately produces IgA. If the individual does not produce sufficient amounts of IgA and is instead IgA deficient, then tTG-IgG should be tested instead.
I was tested just 3 years ago with a variety of symptoms, one of which was anemia. I also know someone whose Kindergartener was having multiple health/behavior problems and we suggested they test for celiac. It is a simple, noninvasive blood test. He tested positive. After a few months of a strict gluten free diet they have a new kid. He was having ADHD type of behaviors that are now better. Speaking for myself, I never realized I had sort of a "brain fog" as they call it from reacting to gluten. If anything it's worth a try to rule it out!
Good luck!