I've been having increasingly worse gastrointestinal problems. Is it possible to suddenly develop an intolerance for specific foods?

Food intolerance. Causes of food intolerance: 1) stomach problems (peptic disease; gastropathy due to nsaid's, sluggish stomach); 2) bacterial overgrowth of small bowel; 3) intestinal malabsorption (due to enzyme deficiency, celiac disease, tropical sprue, more); 4) pancreatic maldigestion (pancreatitis, ductal obstruction; pancreatic insufficiency); 5) biliary problems (gallstones, dyskinesia); 6) ibs 7) colitis.
Yes, possible. Food intolerance (different than an allergy) typically has a dose-response. The more you eat, the worse the symptoms. The symptoms could occur after having the "stomach flu" and the GI tract has not yet healed. This is typical of lactose intolerance with dairy products. It could occur with other foods too. If the problem is fatty foods, the gallbladder may be the culprit. See a GI doc.