。
I was told I have blocked tear ducts.
Literal
Tear-ducts [subject-が] are-blocked [quotative-と] was-told [polite-ました].
涙腺 ('tear gland, tear duct') — 涙 ('tear') + 腺 ('gland'). 詰まる ('to be clogged, blocked, jammed') is intransitive; its transitive counterpart 詰める ('to stuff, clog'). ~と言われました is the passive quotative 'I was told that X' — common for reporting doctors' diagnoses.