If you think you are wheat intolerant, by far the best approach is to eliminate wheat from your diet. This page, about elimination diets explains the best approach to take. It really the most accurate way to work out if you are intolerant of wheat or not.
Skin prick test
You can get your diagnosis confirmed by an allergist or immunologist. Usually, they will use a skin prick test to establish one way or another if you have non-celiac wheat intolerance. In theory, a blood test could be used, but there have been no in-depth research carried out into whether these tests are accurate or not. The RAST test is being studied, and the initial results are promising, so it is possible that particular blood test will prove accurate enough to allow doctors to diagnose wheat intolerance.
Whereas, the skin prick test has been in use for decades, and has been proven to be reasonably accurate. It is important to have it carried out by a doctor. This avoids the risk of the results being misinterpreted.
Home testing for wheat intolerance
So far, I have not found or heard of a reliable home testing kit for wheat intolerance. The only reliable way to find out if you have a wheat intolerance is to follow an elimination diet.
Testing for coeliac disease
If you have been suffering from gluten intolerance for some time your intestines are likely to have been damaged. For this reason, it is possible to diagnose gluten intolerance using a biopsy of the bowel. With wheat sensitivity this kind of damage rarely happens, which means that a biopsy is not a good test for those who cannot digest wheat.