Is it permissible to treat a case of continuous diarrhea and scanty stool, after taking the new colon medication, as urinary incontinence, such that one relieves oneself once before each prayer and disregards any other sensation, or can it be dealt with according to the psychological doctor's advice of ignoring the feeling of passing gas?

The best cure for obsessive-compulsive disorder is to ignore it and pay no attention to it. So, strive to rid yourself of spending a long time in the bathroom. If you doubt that gases have been emitted, but you neither hear a sound nor smell an odor, then your purity is valid, and so is your prayer. Do not pay attention to these obsessions and doubts, for the basic principle is that purity remains until there is proof of something that nullifies it. Your condition does not fall under the rulings of سلس (incontinence/constant discharge).