An immunologist specializes in allergies, asthma, etc. I saw one a year or so ago - refered by my gp - and he confirmed that I have a series of food and chemical intolerances, skin rashes, adverse drug reactions, etc. All he could advise me was to stay away from these things.
But it was the rheumatologist who diagnosed the CFS. Even though CFS is an immune sysem disorder, it is so close in symptoms to fibro, lupus, etc, that it is the rheumie who concludes CFS after he rules out the others.