A few examples that come to mind:
In Emma, upon hearing a lot of unexpected news, her father says something like “good God, after all of these surprises, I think I should go and lie down!” And Emma says “you really should, father, you don’t want to make yourself ill!” I recall the father in The Marquise of O by Heinrich von Kleist being similarly ill after discovering he’s false accused his daughter of scandalous things.
And I’m currently reading The Brothers Karamazov, in which Katerina Ivanovna is experiencing fainting spells and “hysterics” after finding out her fiance’s brother loves her.
The examples you are using are fictional and authors use poetic licence and exaggeration for certain effects.
Woodhouse in Emma is an elderly "Valetudinarian" so is essentially a hypochondriac and Emma, his doting daughter indulges him. In the same book you have Frank Churchill who attacks a group of gypsies which is hardly actions of someone so fragile. Also none of these characters are particularly noble as none of them has a title.
Your second example is an example of 19th century sexism and demonstrates the belief that women were more emotional than men and let their emotions take control of them.
Although, these are merely devices used by the author to highlight certain characteristics of their creations, they must have some foundation in truth for readers to actually believe that these characters were real and to sympathise with them. So yes there must have been some elements in the upper classes who were more emotionally/psychologically unstable, but that would also be true for the lower classes as well. It is just that authors were predominately upper class, as were their audience.
A point on karamazov, his nobility were largely shown as charicatures, as Dostoevsky liked to focus on people's affectations, and he believed the nobility especially to be ruled by those affectations.