I'm wheat intolerant, so I eat a wheat free diet. If I eat wheat my symptoms are: severe stomach cramps, diarrhoea, flatulence, severe bloating (I'm talking looking 6 months pregnant) and constipation. Sometimes nausea. As you can imagine- it's deeply unpleasant.
My life changed once I gave up wheat. I lost over a stone, gained energy and stopped having such problems. I can tell you having diarrhoea everyday is no fun!
I can still eat other sources of gluten with no problems though.
I'm gluten free and grain free by choice since the end of January. I didn't have any gluten or grains at all for 30 days. Since then I've tried it a couple times, but it's just not worth it! I didn't think I had any symptoms from it, but now if I have even a small portion of something with gluten I feel it later with bloating, pain, fatigue, foggy brain, sometimes nausea.
If its just feeling crappy with no other symptoms such as diarrhea, you may want to look into cutting out sugars. Look for low-glycemic diets. Since I've been on low-glycemic, I feel tons better. I tried giving up gluten for awhile, then went back with no difference to me. There are allergy elimination diets where you give up all the foods that frequently cause problems for people, then after a couple months, gradually introduce those foods back in, one at a time, and see if there is any reaction. If you don't know specifically that your fatigue is caused by gluten, it may be worth your while to try to find out what exactly is. Really, if you're not allergic or intolerant to gluten or wheat, there's no need to go without it.