Overall, your draft is okay, but a slight revision is required. It is as below:
a) The very first sentence is compound. Split it into two small sentences.
b) We do not know whether Narotham was hospitalized. Therefore, it is enough if we write, "I have attached a certificate from the doctors stating I was under medication."
c) In the third paragraph, it is enough if we write, "I regret my inability to intimate you through written communication." By the way, is it mandatory to provide written communication despite sickness?
d) In the last paragraph, it is not "condole" but "condone." Secondly, if the sickness was genuine, then the wording of this paragraph is too submissive. It is enough if we write, "In view of the above, I request you regularize my absence by granting me sick/earned leave. I will perform my duties to the best of my capacities once I attain complete medical fitness."
Regards,
Dinesh V Divekar