R.J.
My son has asthma, and got both the stomach flu & a chest cold this week. That, or the same bug that started out with 24 hours of stomach trouble. We've been in the hospital a ton on nebulizers, and I could open a pharmacy with his Rxs. (3 kinds of steroids, antibiotics, albuterol, antipyretics, antiemetics, antiimflammatories).
What we're trying to do is to keep his chest cold from turning into pneumonia and an inpatient stay.
If Finn starts committing his meds before they can work... Ring his doctor. They may have you come in for IV antibiotics, or may have you just keep doing until the stomach part is passed, or hold off for 12-24 hours after the V&D starts. . I can't imagine they'd stop the antibiotic course, though. At least, not for longer than a day. Generally, docs don't play with asthma. 4 minutes until brain damage if his respiratory system goes on strike.
Either way, keep his doctors informed.