Take a look at the original sentence again:
Ursula clutched her head, trying to remember the correct formula to solve
the statistics problem, the only thing she
could focus on, however, was the stupid fight she had in the car with her
boyfriend, Mac.
You chose to fix it the correct way:
Ursula clutched her head, trying to remember the correct formula to solve
the statistics problem; the only thing she
could focus on, however, was the stupid fight she had in the car with her
boyfriend, Mac.
Ursula clutched her head ... begins a complete sentence. The only thing she could focus on, however, was the stupid fight ... starts the second complete sentence. You are always correct when you use a semicolon between the two main clauses that create the comma splice.