That struck me as wrong; because since the character is experiencing it, for them the walls don't seem to be moving, they are moving.
No, the word "seemed" is appropriate, if the character knows they are not actually moving, because hitting their head has impaired their vision system. They know the walls only seem to be moving, they are not really moving.
"The walls began moving" suggests the walls are actually moving; if you want to use that language, then (in first person) you need to qualify for the reader what is really happening.
I stumbled to the ground and hit my head. I got back up. The walls and floors started to move, but I realized this was an illusion, and waited for my eyes to return to normal.
If you have a 3rd person narrator, then regardless of what the character believes, the 3P narrator would use "seem" because the narrator didn't hit their head, they know the reality that the walls only seem to be moving.
Charlie stumbled to the ground and hit her head. She got back up. The walls and floors seemed to be moving, she ignored that and dashed for the door.
Unless you are in dialogue, or writing the internal thoughts of a character (in italics), you need to be careful about what you describe in narration (even in first person). If the character doesn't believe their own senses, they won't report their senses as reflecting reality. Virtually none of us immediately after bumping our head would think the walls are really moving.
This is why, when my character believes something that is actually untrue, I always find a way to state her belief as her direct thoughts in italics, or something she says in dialogue. At worst, my narrator might say "Cindy believed him." I don't want my narrator to state something that isn't true, like "He was telling the truth."
(But I write with a reliable narrator.)
(I think most of us would suspect we physically shocked nerves controlling the eye and they weren't firing properly; thus not compensating for our normal head and body movement to stabilize our vision (like steady-cam technology does), making it seem like the walls were moving when it was our own head moving around. Or we shocked nerves that coordinate our eye movements with each other, which can cause similar issues. At least, those would be my first guesses if a head bump interfered with my vision.)