Doctors who specialize in diseases related to Microorganisms like Bacteria, Virus (Epstein Barr Virus or EBV) and others are Internal Medicine Specialists and also Lemologists (Infectious Disease Specialists).
Most of the Doctors study about infections but when it is related to Chronic EBV infections, the case will be redirected to Internal Medicine depending upon symptoms that are present/progressing/subsiding at that particular period of examination.
Since a Chronic EBV infection has involvement/affects almost every system in the body,where symptoms or presenting condition either through physical examination or Laboratory Investigation are as follows-
Hypersensitivity to mosquito bites
Lymphoma, including B-cell, T-cell and NK-cell lymphomas
Coronary artery aneurysms
As you state that you have Fibro and CFS (Fibromyalgia and Chronic Fatigue Syndrome if I related it correct),which may have multiple causes with underlying etiologies,you will be redirected to an Internal Medicine Specialist , a Neurologist, an Orthopedician (vice versa) who, in association, work with an Oncologist helps you find out the origin of Chronic infection.Post Viral Chronic Fatigue Syndrome which is a complication of EBV must also be considered.
Considering you situation now,I would suggest you visit a Orthopedician or a Neurologist first and let him redirect to concerned department while treating symptoms of Fibro and CFS.
I am not from the US or IL, so I would go to Mayo Clinic who works in collaboration with CDC (every hospital works with Mayo and CDC since they are research institutes).
Please keep us updated on your condition. God Bless!