Should I seek a toxicologist if I have been exposed to black mold, and I'm experiencing severe health problems mainly fatigue and dizziness?

Primary doctor first. For fatigue and dizziness, one should see his primary doctor for a thorough evaluation. Such symptoms are very common and can be due to almost any medical problem. If the primary doctor suspects that the fatigue and dizziness are related to mold exposure, he may refer to an allergist, immunologist, otolaryngologist, or pulmonologist; to look for allergies, nose or sinus problems, or lung problems.
Full workup. Look for another cause, starting with a full history and physical. After over two decades of big-money lawyering, most pathologists and other physicians believe that "black mold" is not a danger -- huge amounts required in animal models. I think the supposed initial cluster was an error. If you buy into a "victim" / "fad" diagnosis like "black mold", you will never feel well again. Best wishes.
Probably not. Black mold has gotten a lot of bad press in the past, but it is not as toxic as you would think. Any mold, with excessive exposure, can cause some irritant reactions, but your symptoms are very non-specific and probably not due to mold exposure.