Hi there, Paulo. "Conk out" would be when someone falls in sleep because he is very tired.
Your polishing of the text was very good indeed, I just would suggest some changes. To some, would be just a matter of style (with asterisk), whereas to others it would be really advisable to redo it. (signaled with ++).
I have difficulty achieving deep sleep...my brother, on the other hand, astonishingly has no difficulty to sleep.
I have difficulty achieving deep sleep...my brother, on the other hand, amazingly has no difficulty to sleep.
I have difficulty achieving deep sleep...my brother, on the other hand, amazingly has none.
I wish I could just go to bed...(but then I am thinking about the everyday habit, your way would do as well, with slight change in meaning.)
And that is when - and that´s when (I would use the latter, but that doesn´t mean that former is wrong. Far from it.)
It has become more prevalent than ever...
(to me it sounds formal and a bit stilted, it´s not by chance that it´s found more in Google Books than in other parts of Google or the Web.)
My choice of words then:
It has become more usual than ever...
It has become more common than ever...
Or even more colloquial, if one wishes; since the text has the informal "conk out" in it:
It has become more and more commom
It has become more and more usual
I become/get infuriated [or ''I get mad/it upsets me that/it makes me feel uncomfortable...(then describe the situation afterwards...)]
...because I do/really want to sleep, but I just can't.
By saying that "I want to go to sleep", to me suggests that there´s someone or something that keeps the guy from going to the bed [perhaps he is at the job, or his brother doesn´t let him. I don´t think such is the case...
On the other hand, if the meaning is an habit, then the expression could and should be used.
So, to the last part of the text, another possible wording could be:
I get mad at myself (or It upsets me that he has no difficulties to sleep, whereas with me it´s the other way around. It irks me that I just can´t get a wink, I hardly sleep all night.
Then, when it is the time to get up, I feel sleepy, tired and with the feeling of being unwell (or really sick, with nauseas, weakness, upset stomach etc...) physically and mentally.
Let´s wait for more comments and suggestions, they are welcome and will enrich the discussion.