Like clockwork, Katherine Moreno gets a cold every year. It always leads to bronchitis, then asthma.

“I don’t go anywhere without a box of Kleenex and an inhaler,” says Katherine, 62, a first-grade teacher who has suffered from allergies since childhood.

For years, she rode out the symptoms and recovered. But after a particularly bad episode four years ago, Katherine’s primary care doctor ordered a CT scan of her lungs....