Just checking on the lamp bulb and tub, so if you've used them with no issues before, then we can eliminate them from the investigation.
Is the chick able to eat/drink on it's own and move around?
Hopefully @Eggcessive will chime in.
Something neurological is possible as @Aapomp831 suggested. I would make sure to give vitamins that contain E and B1 (Thiamine).
Tell me this - have you used that particular heat lamp before with no issues or is this a new bulb? You've used the plastic...