Can your breathing make you sick

Recently I've been getting sick with more vigorous off-bike cardio. I thought it was my diet, or related to fluid intake, or some other things, but now I'm wondering if it was because of my breathing.

Yesterday, while doing the same series of exercises I was very concerted about breathing only through my nose. As a result, I think I slowed my respiratory pattern, and either by consequence or happenstance, I didn't get sick. I know that if a person hyperventilates they can get nauseous, but when cycling and building up more metabolites than usual you need to increase your respiratory rate to breathe off the CO2. So is there a middle ground? Do you who are in the know worry about your breathing?