You are not alone. I have had this occur and it is especially noticeable indoors due to the calmer air. I can sniff the arrow rest and smell it, and also smell it on the feathers if I get to the bag quick enough before it dissipates.
Other "toxic feather off-gassing" experts may chime in with their take, but I have concluded that it is a friction issue from the speeding feather dragging against the rest. In other words, a tuning issue with that particular arrow, or a form issue that induces a tuning issue for that particular shot.
"Aroma Tuning". Well, at least we can brag that our bows really smoke ... and prove it!