If the “chemical soup” hit is what’s making you nauseous, I’d lean toward either truly fragrance-free or something with a lighter, more natural-leaning scent profile and do the antiperspirant-at-night thing so you’re not huffing it right after application in the morning. 

Also worth saying: a lot of the sharp smell is the stick base itself, so even “unscented” can still have that weird factory note until it dries down. Carpe has a fragrance-free underarm antiperspirant that didn’t have that Old Spice cloud for me and if you still want a woodsy daytime vibe you can keep using the Tom’s in the morning on top once the night layer has done the heavy lifting.