Parasites (including Babesia) are known causes of tissue and/or blood eosinophilia. Mold can also cause Eosinophilic Esophagitis (proven in research done at Cincinnati Childrens'). A skilled Environmental Medicine specialist may be more helpful than an Allergist or Gastroenterologist in this context.
As for whether Lyme can cause (or contribute to) EE, I believe Lyme is capable of nearly anything.
For more details about
Eosinophilic Esophagitis, see
apfed.org Note that most MD's will not recognize the possibility of an infectious/toxic exposure cause of eosinophilic disorders.
Credentials: Former Research Director for APFED; Husband has Eosinophilic Gastroenteritis with esophageal involvement.