used it with some egg wash and I must not have cleaned it completely. I took it out a few days ago and it smells NASTY. Like, really freakin gross.

i tried dunking it in soapy water and sanitizer and spraying it really well. Didn't help
I tried leaving it in some soapy water for a day and cleaning it. Didn't help

Is there anything I can do to take the stink out of my pastry brush?
You are correct with your assumption. It is not silicone.