Can you pass out from pain even if you don’t feel it?

I pinched a nerve or something about a week ago. The area between my neck and my shoulder really hurts on one side all the time. Thankfully Tylenol and ibuprofen are helping a lot and I barely feel it when I keep on top of medications.

But I’ve been having a lot of dizzy spells this past week. And even saw stars a few times when doing things that involve me moving my neck or shoulder a lot. So my question is: is my body still registering the pain and injury even though I don’t feel it? Could it make me pass out if I aggravate it too much?