Is it Safe to Avoid Gluten

I just stumbled upon this page in searching for cause(s) of my MANY physical symptoms.

BACKGROUND:
My doctor says it's nothing, but my body says something IS wrong!

Mental fog, back pain, hip pain, joint pain, body aches, exhaustion regardless of sleeping completely through the night, slow digestion, depression, weight gain. . . I am at my wits end.

I've always been healthy, and I basically still am healthy, but every extremity hurts, from my fingers to my toes. If I could rid myself of this pain, I could handle everything else.

I am on an bupropion for depression, Armour thyroid for hypothyroidism, pain medicine due to back pain, all of which help a little because when I'm off of them, my symptoms increase exponentially.

QUESTION:
I want to get to the CAUSE of my health issues listed above, so am wondering if I could safely avoid gluten for any amount of time to see if my symptoms go away? I am willing to try, but don't want to cause more problems.

Thank you!