Student or Learner
Which of the following is correct:
Not only he but also his brother has his problem.
Not only he but also his brother has their problems.
As for the OP: I find both sentences awkward, because if you remove the words "not only" and "but also his brother," you are left with "he has his problem." That seems awkward and redundant to me; of course he has his problem, whose problem would he have? I assume your reader already knows what the problem is. If so, you could write, "not only he, but also his brother, has that problem."