Take a look at the sentence again:
When Jim threw his back out while helping his wife Nancy move the sofa,
he feared the treatment the doctor would recommend,
a week's worth of bed rest during the nicest week in April would
certainly wreck Jim's golf plans.
The problem occurs between recommend and a. He feared the treatment the doctor would recommend is a complete sentence. A week's worth of bed rest during the nicest week in April would certainly wreck Jim's golf plans is the next complete sentence. Because these two parts have just a comma between them, they create a comma splice, a major sentence error.
To fix the problem, you could put a period after recommend and then capitalize the A.