The problem is due to the common mucous membrane immune system. The elevated TNF and IgE levels cause hypersensitivity to a wide array of irritants including common bacteria and allergens. I imagine that nutrient deficiencies resulting from malabsorption also contribute. Oxidative stress is poorly controlled because vitamins E, A and C are commonly deficient as are zinc and iron. Malabsorption also results in calcium deficit and taking calcium carbonate has the effect of reducing stomach acids thus diminishing the ability to absorb other deficient minerals (and carbonate is the least absorbable form of calcium, if also the cheapest). Of course, the teeth reflect the state of the calcium supply in the body, so they suffer as well. Malabsorption is a consequence of inflammation of the ileum and excess mucous secretion and commonly causes B12 and folate deficiency as well.
There are a number of syndromes relating to immune reaction to gut bacteria (the currently accepted view of the process of Crohn's) resulting from the immune cascade (TNF and IgE and a host of immune molecules) and the bacterial response (gut infection, release of endotoxins, diarrhea, fistulas and fissures, increased gut permeability, translocation of gut bacteria to the blood, liver, gallbladder, pancreas and others) and mimicking of body tissues by gut bacteria or their by-products resulting in auto-immunity toward a wide range of body tissues (mostly mucous membranes like the synovia).
To answer your question, throat, mouth and sinus lesions result from chronic inflammation of the gut. Even in well-controlled Crohn's, there is commonly irritation in the throat and sinuses.