If you are having a blood test done, then I believe that it is just an IgE "marker" they are looking for which should be present whether there is gluten in your system or not. You can get home tests, I know you can get them in Canada but the company I know will not ship outside of Canada. There must be a similar product in the UK although I have never looked. If you google for it you may find one. It's not 100% accurate but it is a good start.
If you are having a bowel biopsy done (which is the ONLY accurate way to diagnose celiac for 100% certain) then if you have gone onto a gluten free diet and the bowel has repaired itself then it can cause false results. So in this case you need to be eating a "regular" diet for a time period before the bowel biopsy.
Probably the best way to do it is go gluten free for your son for a time period and see if he changes, and ask the doctor for a blood test.
The thing is, at this age lots of LOs are windy and have loose bowel movements, 1-2 a day is normal I think, and eczema and nappy rash aren't really signs of celiac disease -- just toddlers. Windiness can be caused by lots of foods and it might just be his body getting used to digesting them as his system is still young an immature. Foods like beans, cabbage, brocolli, etc all cause windiness! Eczema can be food related or environmental or even just sensitive skin. I wouldn't worry if those are his only symptoms - they seem really toddlerish rather than celiac. IMO!