Sorry to hear about the neck issue. This sounds like a fairly typical presentation of acute neck pain (sometimes called acute torticollis or a “wry neck”). While the pain intensity is often very high and the loss of range of motion is frustrating, the natural course or history of this is pretty good. It mostly resolves on its own in a few days to a week.
The fact that you were able to deadlift with 2-3/10 pain is certainly a good sign. It demonstrates that despite the sensitivity and “locking up” sensation, your were able to to handle significant load.
That is the winning strategy here: find the movements you can perform tolerably and do them, rather than focusing on the range of motion you currently lack.This is covered here (and you may be familiar with it):
https://www.barbellmedicine.com/blog/pain-in-training-what-do/
And common mistakes to avoid:
https://www.barbellmedicine.com/blog/lifting-rehab-mistakes/
If you want a specific programming adjustment or a professional evaluation to manage this, you would need to consult with our Pain & Rehab team directly:
https://www.barbellmedicine.com/shop/coaching/pain-rehab/injury-rehabilitation-management/