Can over proofed dough be harmful to breathe in?
.... There's no way to know for sure (since we can't test it) but it was probably CO2 (Carbon Dioxide)... Yeast creates CO2  when it converts sugars... that's how you can bottle carbonate beers. 


  The breaking down of sugars, or fermentation, produces alcohol and carbon dioxide as by-products. Fermentation turns fruit juices into wine and helps turn wort (diluted grain mash) into beer or whiskey. The carbon dioxide produced by fermentation makes the bubbles in beer and some kinds of wine, and causes bread to rise. As bread bakes, the alcohol produced by fermentation evaporates.


We brew beers and we've had our freezer, which we use for a fermentation fridge, fill with the gas when we're brewing and the fermenting overflows. When we have to get into the freezer to clean it out, we have to be really careful as the carbon dioxide is heavier than air, so it stays in the freezer for a while... the same thing would be true of your large, covered mixer bowls. It can make you light-headed because your brain is suffering from oxygen deficiency.

Here's the fact sheet on CO2 inhalation:


  
  Inhalation: Low concentrations are not harmful. Higher concentrations can affect respiratory function and cause excitation followed by depression of the central nervous system. A high concentration can displace oxygen in the air. If less oxygen is available to breathe, symptoms such as rapid breathing, rapid heart rate, clumsiness, emotional upsets and fatigue can result. As less oxygen becomes available, nausea and vomiting, collapse, convulsions, coma and death can occur. Symptoms occur more quickly with physical effort. Lack of oxygen can cause permanent damage to organs including the brain and heart.
  


And, because it's a byproduct of the yeast activation, it can smell really strongly of yeast, and have a really off smell, despite the gas itself being odorless.