Can you go to Home Depot and buy two big cardboard boxes and just tape them together to make a larger brooder maybe 3’ x 5’ for a few days until you were done building your outdoor coop and enclosure? If you put them outside, just make sure you buy a ceramic bulb, that’s what I used, they don’t give off light only heat. Your chick will not be able to be picking at her in the dark I do not think. Is your silky a white chick? I don’t know but I just thought that maybe your bulb is making her feathering appear red since the color of the heat lamp is red, maybe that is stressing that other chick out and causing her to pick at her.