To call ourself slave of Prophet Muhammad (salehalawaalihiwasalm) is allowed
It has been narrated in 'Sharhus Sunnah' from Ibne Munkadir that the slave of the Beloved Prophet (Salla Allahu ta'ala alayhi wa Sallam)' Hadrat Safina lost his companion in Rome or he was arrested. He escaped and was searching for his friends; at of a sudden he saw a lion in front of him, so he said, '' O Abul Harith (Lion) I am the slave of the Beloved Prophet (Salla Allahu ta'ala alayhi wa Sallam) and I have faced such and such problem. Listening to this the lion came near him and stood by him. Whenever the lion heard a voice he went to that place and stood, again and again, he just used to walk up to Hadrat Safina (Radi Allahu ta'ala anhu) until he reached his companion.
[Hadith in Mishkat Shareef Page 545]