I would say that your analysis is good, but there are places where your grammar could be a little more rigorous, your sentence structure more concentrated and language more concise, for example:
I fundamentally believe that it is natural for the reader to sympathise with Jekyll as his intentions were simply to feel liberated from the inheritance of humanity. He therefore concluded that “man is not truly one, but truly two”, of which one fears to expose the worse part, as it would result in societal ostracisation, such is the unforgiving expectation to be completely free from scandal. A sense of urgency is conveyed through his radical use of transcendental science to separate the components of his personality into two separate beings, and that he is ashamed of his selfish “desires”. However, Jekyll felt restricted by pressure to adhere to social conventions and the law. It could be argued that he wanted to expose himself fully to remove the guilt that he feels for hiding the insidious elements of his character to gain social advantages. This makes the reader consider the duality that exists within them, and therefore makes them feel embarrassed. Furthermore, one could argue that Stevenson uses the novella to criticise Victorian men who outwardly display noble qualities in order to gain public approval, while hiding rogue elements of the personalities, by representing each part by the characters Jekyll and Hyde.
NB: I have also reordered it a bit so that the argument is more coherent.