As asinine a statement as this may sound, with children anything is possible. This is mostly because children don’t have the same amount of knowledge about hygiene as adults do and why it is necessary. To come back to your question, sugar consumption cannot cause worms at all. However, from your question, one can judge that the child in question is suffering from some sort of diarrhea or discomfort. This can be because of two reasons: the child is fructose intolerant or that the sugar consumed was contaminated by some kind of fecal matter that further leads to worms in the intestines. Both of these conditions are curable and your child should be fine if you follow the requisite treatment.
Fructose intolerance is a hereditary disease and is a possible reason for a child to feel malaise. The condition is not normally associated with getting diarrhea. The problem in this condition is an inability of the body to produce the enzyme aldolase A. This converts fructose down to glucose from a complicated set of chemical reactions. The symptoms that occur with fructose intolerance include hypoglycemia, jaundice, hemorrhage, and sometimes kidney failure. Fructose is used quite widely in many carbonated drinks and simply staying away from them and fruits will solve the problem. In the case of worms, worms require a fecal oral route of transmission. Most worms reproduce in the gut of an infected human and end up in human feces. From here, through contaminated water sources or through handling soil that is contaminated with feces and not washing afterwards, worm eggs will end up getting into the stomach. There are some more incredible forms of transmission of some types of worms. In Africa, merely standing in a pool of water that is contaminated with worm eggs is enough to get the worm. This happens because the worm burrows through the skin of the feet to travel to the gut.
What you need to do is to ensure that your child is treated for a possible worm infection. First see a doctor to confirm diagnosis with a stool sample. If this is the case, your child will be prescribed albendazole or variant of it. At home, feed your child a teaspoon of clove oil, an hour before every meal and after meals to chew throat lozenges that contain hexylresorcinol. Both these are anti-helmintic or toxic to worms and can help in consonance with the doctor’s prescription.