White rice is not problematic because of fructose. White rice milk might cause constipation if you have FM or not.
Like said, in FM, it is a low-fructose diet, not necessary fructose-free diet, recommended. The amount of fructose someone can tolerate varies a lot from person to person. Search for "nutrition guide in fructose malabsorption" to find foods to try and to avoid.
Besides fructose, polyols (sorbitol, xylitol, maltitol...) used as sweeteners, fructans in wheat and onions, fructooligosaccharides (FOS) and HFCS are often problematic in FM.
I've interviewed several people with FM ad quite some cannot tolerate sucrose, despite its gluctose:fructose ratio 1:1.