Welcome to NeuroTalk:

Going gluten free should be a longer trial for you. Being low in many nutrients suggests you need to be gluten free much longer...a year or more. Malabsorption of nutrients is one sign of gluten issues. Once you determine your issues are from gluten, then gluten free is for life.

Recovery can be slow. And yes we've had over the years PNers who were positive for gluten. Some have moved on to the Celiac communities as their PN resolved. Gluten free becomes a lifestyle and there are places online for just that.

Our board here has some threads about testing:

http://neurotalk.psychcentral.com/thread138655.html

This link of jcc is very complete with tons of information:
http://neurotalk.psychcentral.com/thread1872.html

Yes, you should be eating gluten for any blood testing. And from what I have read over the years, the longer you go gluten free, the more you will notice reactions to slips or hidden gluten in foods.

There are other foods that can cause burning... MSG, a food additive, I get burning from nightshade veggies (potatoes, tomatoes etc), and some people have histamine release from certain foods.
http://www.allergyuk.org/fs_histamine.aspx