I am not aware of any feasible way to raise cholesterol, but you can take Pregnenalone to support your adrenal function.
The late Dr. Richard Van Konynenburg did some interesting research on Chronic Fatique Syndrome. His theories are based on the idea that the problem starts with some sort of infection (lyme, EBV, parasite, etc) and the low cholesterol is due to the bodies response to the infection. He used Dr Amy Yaskos protocol for Methylated vitamin therapy (active b vitamins) to raise Glutathione in the body.
I would recommend you read some of Richard's work as well as Amy Yasko. These may be a good foundation.
Dr Mark Hyman has some good articles as well discussing how infections in the gut can lead to an array of complex medical problems.
Your situation resembles a parasitic infection. Strongyloides causes bloating and can create a Celiac like syndrome.
It is one of the only clinically proven causes of gluten sensitivity or celiac in previously healthy people. Another symptom of this can be slow digestion, constipation or blockages.