I think Vert art dissection is pretty rare, but can happen with many day to day activities according to the list here..- A lot of info on symptoms and treatments too.
https://my.clevelandclinic.org/healt...ery-dissection

One medical site even stated the neck pain/symptoms that may cause a person to go to a chiro might have been the VAD before any adjustments..

Did you have a specific injury or event that gave you the original neck & back pain , or was it more of a ongoing and increasing pain?

Did it seem that the chiro was new , overly rough or jerking with adjustments?

It could be a pinched nerve more than VAD by the symptoms, but I don't know , but you might consider a more expert chiro?