It is important, if you want the the testing done for Celiac disease, not only to keep gluten in his diet but ensure he is eating plenty of it...a few pieces of bread a day, for example.
My toddler has Celiac disease. Her symptoms were on the more radical side...constant, bulky, fatty stool throughout the day (talking twenty diapers a day), bouts of pain that would last 3-4 hours and have her literally screaming and rolling on the floor, inconsolable, and dermatitis herpatiformis, so bad that it looked like her skin was rotting. From ages 7-11 months, she did not grow...not one ounce, not one centimeter. She also did not smile, did not laugh, did not play...she just screamed. Cried. Thrashed.
We had to push and push for the testing, but her ped. wanted to test for about 50 other things first...so I just took her off gluten. It was like a miracle change in my baby...within two days, I saw her smile, I heard her laugh, and could hold her without having my eardrums busted.
They agreed to test her after that, but I absolutely could not get her to eat anything with gluten at that point. I tried it all...cookies, cake, everything...and she just wouldn't eat it. It's like she understood. Her test results, when tested several weeks after being gluten free, were STILL high...so she has a clinical diagnosis of CD. I refused to have a biopsy done because I have my answer and will not put her through that just for confirmation...I have all the confirmation I need, and several doctors agreed.
As far as the diet goes, it can be as simple as concentrating on whole foods...fresh meat, dairy, fruits, veggies, rice. If you want replacement products, such as bread, pasta, waffles, cookies, cake, etc, you have the option of buying GF or making your own. I have my favorite brands...you can ask again when and if you go GF and I'd be happy to share what I love and hate with you.
As we have gone along over the last two years, I have virtually changed almost everything about the way I feed my family. I make everything from scratch, I know where my food comes from and what it's made from, we buy almost no processed food...and we ALL feel better.
Because I nursed her until she was almost three (just weaned a few weeks ago), I was GF as well. I was so excited that I could now eat some "real" bread, pizza, etc, and I dove right in...and immediately began getting the same debilitating migraines that miraculously "disappeared" while I was nursing her. So I suspect that I have a sensitivity, and have given up on having gluten (maybe on rare occasions...) because after over 2 years, I no longer miss it and don't want the headaches.
If you can't get him an appointment right away, I agree with others that have suggested to just remove it from his diet and see if YOU see an improvement. You'll see it VERY quickly if he has CD, but it may take a bit longer if it's just a sensitivity.
Read up what you can...there are a lot of books suggested below that will be very helpful. It's important to learn about contamination, cross-contamination, and hidden sources of gluten. You need to learn about US regulations regarding food labelling and the difference for imported foods (which may say "gluten free" on the front and "contains wheat" on the back...). You need to get used to calling companies to inquire about the GF status of foods if you aren't sure. It's a process, and expect that you will occasionally mess up. We all did while we were learning, I can guarantee you, but you will get it all figured out.
If you'd like any more help or have more specific questions, please feel free to pm me. Good luck!