Vertigo usually is not a symptom of mononucleosis.
The vertigo you experience might be related to pain in the ears which might have been ear inflammation. You might want to visit an Ear, Nose and Throat specialist for ear exam. If ear infection is found, adequate antibiotic treatment will be recommended. Once the infection is treated, it might take up to several weeks for the vertigo to stop, if no irreversible damage was done to the ear structures.