I doubt it means anything which translates into modern medical knowledge.  That's from a period when very little was known about the brain, and frontal lobotomy's and blood-letting were recognized cures for real medical problems.  I'd say it means her brain was all clogged up, big time.  With what?  Grey matter??

It's possible that records of her symptoms still exist which enable doctors to make an educated guess as to what her affliction was.  "An accute congestion of the brain" is undoubtedly sheer bull, although the doctor who created the expression may have envisioned something in his own "brain."

I see your web reference mentions "meningitis," which is an inflamation of the brain, known to cause these permanent sensory losses in severe cases.

Edit.  Lest I be responsible for creating misinformation, frontal lobotomies are much more modern than I thought   -   1939 to 1951.  Helen Keller would have been age 19 months in 1881, 58 years before the first such brain operation.