I have never had an "official" diagnosis - I had, however, had bowel issues from since I was a baby, non-specific in many cases but by the time I hit 30 I had quite bad IBS - sudden intense cramping that saw me needing to find a loo Very Fast while shopping, that kind of thing, and general bowel disruption.
Wheat intolerance is quite a common trigger for this so I gave it up - never been happier! Took less than 2 weeks for the IBS symptoms to go away, and sundry other issues such as frequent migraine, acid reflux/indigestion, tiredness after eating, nausea after eating. All gone. Unless I have wheat - in which case they start to creep back - specifically the acid reflux and IBS, plus I get terribly puffy under my eyes. I don't usually get the sudden horrendous attacks that a coeliac would if exposed to a little bit of gluten; I can "get away with" a single biscuit sometimes but if I do it again a second day I'll pay for it.
I cannot be arsed to be tested, in all fairness - I doubt I would test positive but I am not putting myself through 6w of being back on the wheat (misery!) as it would have no actual benefit to me to "know" - what I already know is good enough for me.
Also, I never had a dairy problem, ever. Still don't.
While lactose intolerance is not entirely diagnostic, it does point to small bowel damage, because the lactase enzyme is produced in the small bowel by the brush border, which is destroyed with the villi by the autoimmune reaction to gluten that occurs in coeliac disease.
Gluten intolerance - well gluten is found in wheat, barley, rye and oats. The gluten molecule in the first 3 is quite similar, and the avenin in oats is rather different, hence some coeliacs can tolerate oats but others can't. So I suppose you could work it out by finding out if you can tolerate barley and rye but not wheat; or if all of them set you off.
As it happens, I steer clear of barley as well but generally of the malted variety - beer and whisky make me awfully ill, even just small amounts! 
Hope that helps!