The tTG IgA test is not the most sensitive test for picking up cases of celiac disease. According to the World Gastroenterology Guidelines for Celiac Disease, it only picks up 75-95% of all celiac cases - it could miss up to 25% of celiacs.
As you know, celiac disease can lead to low B12. It is extremely common. It could takes months on the gluten-free diet for that to improve though. If you think you will have a hard time committing to the gluten-free diet, and you need to be 100% committed to get the full health benefits, then you should probably continue eating gluten and get further blood testing or an endoscopic biopsy done. The link above, on page 12, has all of the serologic tests done for celiac disease. The DGP tests are some of the best.
There is a good chance you have Non-celiac Gluten Intolerance /Sensitivity (NCGI) in which case there is no blood test that can diagnose it, only a positive reaction to the gluten free diet is diagnostic. You would need to commit to many months gluten-free to notice all benefits, I would consider 3 months the minimum and 6 months would be better. NCGI can lead to low B12 too.
I know it's hard to have a plan of action when you feel badly but you need to make yourself choose a path, be it going gluten-free now or pursuing further testingand then going gluten-free, and commit to that path so you can move towards better health. It is so very hard to get started but once you get some momentum going it gets easier... at least that is what I have found.
Hang in there.
Thank you so much for all the information. I haven't decided what I want to do yet.