What does it mean to "feel Humpty"?

Solution 1:

'Getting the hump' and 'humpty' are common Cockney or London expressions for being annoyed or disgruntled. My mother's family were Cockneys.

Solution 2:

My father (From Birmingham England) used the term 'feeling humpty' for feeling unwell, which figures, as in the nursery rhyme Humpty Dumpty has a great fall and can't be put back together again.

Solution 3:

From Wikipedia: https://en.wikipedia.org/wiki/Humpty_Dumpty at Origins

"...According to the Oxford English Dictionary, the term "humpty dumpty" referred to a drink of brandy boiled with ale in the seventeenth century.[8] The riddle probably exploited, for misdirection, the fact that "humpty dumpty" was also eighteenth-century reduplicative slang for a short and clumsy person.[11] The riddle may depend upon the assumption that a clumsy person falling off a wall might not be irreparably damaged, whereas an egg would be. ..." [my emphasis]

Your meaning could be either short or clumsy depending how well each fits the context of the dialogue.

Taking the idea of reduplicative slang a little further, and as is noted above in the comments, possibly empty.