I had multiple colonoscopies while having active Ulcerative Colitis/Crohn's Disease without incident. Also my sister, also my brother (inflammatory bowel disease "runs in families" and it definitely runs in mine).

It appears that the GI doctor thinks your symptoms are concerning enough to do both types of tests in order to make a diagnosis. While you can have other types of studies and images, they can't get a biopsy. For some conditions - like inflammatory bowel disease, cancer, diverticulitis, and others - you need to have a biopsy for diagnosis. For some things, like colon polyps, the polyp can be removed before it develops into something.

You definitely want a doctor who does a lot of these procedures to do yours, and that would be a GI doctor. You would certainly want a definitive diagnosis before starting any kind of treatment, traditional or functional. You may want to be treated by a functional medicine doctor once you know what is going on, but I expect they would also need to know what you have for effective treatment.