Chronic mouth ulcers are relatively common, especially in young people. It's called apthous stomatitis, affects at least 20% of the population, and its natural course is one of eventual remission. By far, most people with apthous stomatitis are otherwise healthy.
However, when someone presents with recurrent mouth ulcers, one should always inquire especially about the opthalmic, genitourinary and gastrointestinal health of these patients, because (ignoring the first two organ systems) apthous stomatitis is more commonly seen with Celiac Disease and Crohn's disease.
Common Causes of Chronic Diarrhea
Irritable Bowel Syndrome (IBS): (most common) caused by (?) bowel wall muscle dysfunction
Inflammatory Bowel Disease (IBD): caused by structural damage to the intestinal mucosa that impairs absorption and stimulates secretion
Malabsorption syndromes: carbohydrate, bile acid, etc.
Chronic infection: C. diff, giardiasis, small bowel bacterial overgrowth, parasites, etc.
Celiac Disease (wheat/barley/rye protein-induced autoimmune disease)
Endocrine diarrhea: from hyperthyroidism, Addison's disease, gastrinoma, etc.
Idiopathic Secretory Diarrhea
Common symptoms associated with chronic diarrhea
In IBS and IBD, the patient typically has crampy, intermittent abdominal pain relieved with bowel movements. In IBD and Celiac Disease, stool often occult heme+.
Malabsorption (eg, lactose malabsorption) and maldigestion (eg, pancreatic insufficiency)is typically associated with onset of diarrhea soon after eating and/or relief with fasting.
I assume your doctors have already looked for Crohn's (it appears they've looked for signs of Ulcerative Colitis as well.) Endoscopy and colonoscopy may both miss Crohn's, however, because - unlike UC - Crohn's can skip around in the small intestines; though it is most common in the ilium (the terminal portion of the small bowel) and the proximal colon, it can cause ulceration anywhere from the mouth to the rectum. It can come and go with remissions lasting for years, and, interestingly, Crohn's is often accompanied by abdominal pain and feelings of low energy and fatigue, as well as possible weight loss and malnutrition. Celiac Disease can present in a mild form with only unexplained iron deficiency anemia (from malabsorption) to chronic diarrhea with fatigue and weight loss.
Also interestingly, Crohn's responds to anti-inflammatory drugs, though the wrench in this scenario is that NSAIDs usually make it worse, not better.
Inflammatory Bowel Disease is a difficult problem, but there are effective treatments for Crohn's. Irritable Bowel Syndrome is a common cause of episodiic diarrhea (sometimes alternating with constipation). IBS can come and go as well.
There are new tests for Crohn's (e.g. fecal biomarkers) and IBS.
If by no food allergies you mean you've had skin testing, then true food allergies have likely not been ruled out, as skin testing is not reliable. Celiac Disease is diagnosed best by positive serology, positive small bowel biopsy and a favorable clinical response to a diet eliminating wheat gluten/gliadin (and perhaps barley and rye as well.)
What can someone with persistent symptoms without a diagnosis do?
First, they can try an elimination diet. A person can do that without seeing a doctor. Also keep a food diary. That's always a good idea with any gastrointestinal problems.
They might talk to their gastroenterologist about different trials. Since you have no definitive diagnosis, a "step-up" approach seems more prudent.
Irritable bowel syndrome (IBS) - Causes
ABC of oral health: Mouth ulcers and other causes of orofacial soreness and pain
Recurrent aphthous ulceration: vitamin B1, B2 and B6 status and response to replacement therapy
What is Crohn’s Disease?
Celiac Disease: Celiac Sprue, Gluten-sensitive Enteropathy
Gluten-Sensitive Enteropathy (Celiac Disease): More Common Than You Think
Prevalence of Celiac Disease in At-Risk and Not-At-Risk Groups in the United States
Yield of Diagnostic Tests for Celiac Disease in Individuals With Symptoms Suggestive of Irritable Bowel Syndrome
Eradication of small intestinal bacterial overgrowth reduces symptoms of irritable bowel syndrome
Almost everything you could possibly want to know about food allergies can be found in one of the Guidelines for the Diagnosis and Management of Food Allergy in the United States at this link.