Meaning of "how I was put together and where things easily came apart"?

Hello everyone. I am reading a novel, and I came across this expression. Could you please let me know its meaning?

What made things worse was the shame of it. Was there anything I could do to dispel the indignity of being just a writhing human body? I tried to comfort myself by spinning feel-good platitudes—that our body is who we are, that our body knows us better than we do, that showing all was far better than my smokescreen of words, that this went to the heart of things. But I couldn’t bring myself to believe it.

Or perhaps things were more complicated than I thought. For part of me liked nothing better than to show her how I was put together and where things easily came apart—the thrill of laying myself as bare and open as an anatomy book where you lift one transparency after the other to show the color of fire in my gullet and of the quiet hysteria coiled around the telltale organs of shame, the pleasure of my shame, of my petty, paltry, startled shame—a shame one puts on and tries hard to believe exists and even struggles to overcome, when, all along, as in nudist colonies, it was left in a locker with our watch and our wallet.

- André Aciman, Eight White Nights, First Night

This is a novel published in the United States of America in 2010. This novel is narrated by the nameless male protagonist who meets Clara at a Christmas party in Manhattan. But, at the party, the protagonist accidentally swallows a very spicy appetizer and now is sweating hard in front of Clara. He tries to calm himself down, to no avail.

In this part, I wonder what the underlined expression means.

My wild guess is that he tried to organize himself (=put together), but then I wonder how he wanted to show that the things easily came apart. Thank you very much for your help.