Woe is the overflowing email inbox! But how to complain properly, so that your word choice doesn't distract from the valid issue at hand?
The correct answer is "a) She has fewer emails than I do."
Want the easy way to know which to use? Ask yourself if you can count the item in question. If you can count the number of emails, then it's "fewer" but if you're saying "She has less work than I do," it's because you can't itemize and count "work."
Bonus examples:
He has less food than the others. He grabbed fewer sushi rolls than his co-workers.
She has less time to complete the task than her colleagues. She has fewer hours until the deadline because of her customer's late request. I hope it's not a picky customer, since rush jobs tend to show!