My LO does the exact same thing so we've resorted to a very thin flat pillow in our bed for her under the sheets.
Same, she just loves pillow till she falls to deep sleep then we can take away .tho ours are also very flat and seems working.
I have noticed the same thing with my little girl when she also comes in my bed every night after crying when she wakes in hers 😫 I haven't tried a pillow but my friend has a baby same age and I know they use a special toddler one
My little girl sleeps with a comfier ( a little teddy like thing) and no matter how many times I put it on her arm she walks up using it as a pillow. Because it's suuuper thin I don't mind her using it as a pillow. I think if I were to consider a pillow like thing to help his sleep I would find a small thing blanket or even pillow case and fold it up placing it UNDER the cots fitted sheets. That was he's not likely to accidentally pull it over his face. (I hope this makes sense as I don't have my glasses on and can't see what I'm typing lol)