Is there a correlation between sjorgren's syndrome and eosinophilic esophagitis?

None. No. In the primer of rheumatology and a quick pubmed search, no relationship.
Not specifically... Eoe has recently been associated with connective tissue disease but not specifically sjorgen's. See below http://www.Aaaai.Org/global/latest-research-summaries/current-jaci-research/eosinophilic-esophagitis-connective-tissue-disorde.Aspx.