You can be tested for celiac disease initially by a blood test for gluten antibodies. Basically people with this illness respond to gluten as if it were an invading pathogen and the immune system attacks it. That immune attack makes you feel sort of sick because it cause inflamation. What is worse is that the immune system gets confused and starts to attack your small intestine. This causes atrophy of the cells that absorb food nutrients so a lot of what you eat is malabsorb and ends up in your colon for the yeast to feast on. Some people get diarrhea, some get constipation, some lose a lot of weight but that usually only happens in severe cases. Most people spend several years or more being told they have IBS or some other hard to diagnose/hard to question bowel upset. The malabsorbtion causes general illness because you aren't getting all the nutrients you need for health. You crave food because you aren't getting the food your body needs where it needs to go. Mineral absorprtion is also messed up so some people (especially older women) get osteoporosis. Skin isn't as nice as it could be and wound healing can be slow.

If any of this sounds like you find a doctor who will give you a celiac panel blood test
antigliaden IgG & IgA (gliaden is the specific protein in wheat that causes the problem)
antitransglutaminase IgA (one of the self proteins that the immune system attacks)
total IgA (people with celiacs are sometimes low on total IgA antibodies and so show a false negative on the IgA tests)

Those are the minimum blood tests. If any come back positive you could have celiacs. A biopsy of the small intestines can be done to check for damage (a scope goes in through your mouth under light sedation). If you do have celiacs than the only treatment is to eliminated ALL gluten (found in wheat, rye, barley and oats) and never eat any amount of it again. This can be challenging but the diet has saved many lives.

If your doctor says you can't have it because it is a rare childhood illness he's/she's wrong. A study has shown that in random testing 1 in 250 people have celiacs disease and many are undiagnosed. Do some websearching. There is a lot of info on the subject and if it sounds like it might explain how you are feeling then see a doctor that can at least order the blood tests.

I would not advise going gluten free without testing (you have to be eating gluten for the tests or they will show up negative) because the diet takes a fair amount of effort and committment. Gluten can be found in many many products including many of the low carb products. Cross contamination is an issue too. It is better to know ahead of time whether the effort is worth it.