I can now, finally, take a short break.
"Recently" expalins when the exams happened.
To "take" an exam. To complete, to undergo, to sit, to do.
It should read "one exam after another" - (another example is "one problem after another") and the noun (exam) doesnt require an "s" - it is singular.
I've added "now" to show that, at this present time, you are currently taking a break. I have also added some punctuation to the sentence.
I have also reversed the sentences, so that the first one explains what has happened (in the past) and the second explains what is now happening (in the present). This seems clearer to me.
I am not a teacher. These are just my opinions and thoughts.
Student or Learner