"Travesseiro" is a bed pillow and "almofada" is more like a sofa cushion...although I think either should be fine here because this sentence makes absolutely no sense! (Unless it's a Brazilian expression...?)
From a pillow of the winds: https://youtu.be/wFt99jcazHs. (A nice early Pink Floyd song with portuguese subtitles. There are interesting cognates, relating to our topic, right at the beginning: eiderdown = edredom. They don't seem having a Latin origin. Maybe Celtic ??? )
Interesting. In Portugal they use almofada, my wife (from Coimbra) says she never uses travesseiro. It should probably be accepted as well. Maybe this sentence has a sensuous meaning, you know "Don't worry baby, my pillow does not speak ..."
I'm really confused about the rules on word order, especially in negative sentences. I had a different order from that of mikeanayaus which was also marked incorrect: Não o meu travesseiro fala. Any guidance?