S.A.
She 10 months old, there is nothing else for her to do except throw a tantrum because she is frustrated...she can't talk to you and tell you what she really wants yet.
Sure give her that pillow and blanket (if its your pillow it probably smells like you and she just wants to have you around all the time).
If you take away something she likes or something that is unsafe for her to be playing with, entice her with a different toy or activity.
Just think, how do you want to remember the way you put your child to sleep at night-with her screaming or with her comforted by this pillow and blanket.
We all have security issues, even as infants. This is her security blanket/pillow!
If you feel unsafe with the pillow in the crib at night, take it from her AFTER SHE FALLS ASLEEP!!!