The only correction is to change Since three days, I have been not getting sleeps due to exams.
to
For three days, exams have kept me from getting enough sleep.
The rest is fine.
usage of phrasal verb conked out
I worked hard today. After returning home, I conked out on my sofa
Since three days, I have been not getting sleeps due to exams. Finally, after exams I conked out continuously for six hours.
2 answers
it sure is grammatically correct but not with few errors....instead of saying "since three days", "for three days is more correct"....therefore saying "for three days, i have not been getting enough sleep due to Exams" is good