Brain fever is most likely either encephalitis or meningitis. Both of them are very serious illnesses that require immediate and often intensive care. There is also a risk of permanent neurological damage, which may be why characters in novels who’ve had brain fever seem to be ‘not quite right’ or have a very lengthy convalesence.
My own theory is that Beth from Little Women died of heart failure because of the scarlet fever clue. This can develop into rheumatic fever if left untreated, (and there wasn’t much one could do about it until fairly recently) and this often causes scarring of the heart. My grandmother had rheumatic fever as a child in the 1910’s and had heart problems directly related to this childhood illness all her life, requiring open heart surgery twice. It eventually killed her, and she died of- you guessed it- heart failure. I’m way too lazy to dig out my copy, but if you like you can see if there’s any description of Beth’s symptoms that might match heart failure, like difficulty breathing, blue lips and cold limbs from poor circulation, weak and rapid pulse, swelling of the limbs, and a general progressive weakness. People suffering from heart failure often have to sleep propped up because of fluid build-up in the lungs.
IIRC, I believe some people with certain types of diabetes can experience skin problems, although don’t take my word for it.
Tuberculosis (consumption) was a major killer, especially in industrial areas, during the 19th century. It was oddly romanticized for some reason, and sufferers were described as beautiful and luminous, when in fact they were extremely pale, lost almost all body fat, often sweating, struggling for breath, and coughing up blood as their lungs more or less disintegrated. In old medical journals, TB symptoms at autopsy are extremely unpleasant, as the lung tissue is covered with hard nodules and adhesions.
Other diseases that crop up in novels tend to be childhood illnesses that devastated populations in pre-vaccination and pre-antibiotic eras. Rickets, or deformity of the long bones due to poor nutrition and inadequate sunlight is often mentioned, though it rarely killed in itself. Polio turns up later, and other contagious diseases which were former killers such as measles, mumps, whooping cough, and diptheria.
Cholera turns up in novels of the mid to late 19th century, or novels set in India. Earlier novels often feature various fevers, usually unspecified since they could not be diagnosed, and for infants ‘failure to thrive’ was common, in which a baby or young child simply seems to waste away for no clear reason.
Even earlier novels, particularly of the 18th century, feature true epidemic killers like smallpox and typhus, which had names like gaol fever and shipboard fever. Women often died of peurperal fever, or purples, after childbirth.
Even earlier you get into things like plague and leprosy.
You also read about people ‘having fits’ or ‘taking fits’- this could be epilepsy, or symptoms of something like meningitis, which can cause convulsions, as can very high fevers.