Aug 23 - about reflexive verbs

I understand the following three sentences.

1. Me hablo.

2. Me levanto (a las 6:30 de la mañana).

3. Me acuesto (a las 11:00 de la noche).

And I also understand the following two sentences.

1. Lavo la cara. = I wash the face. (But it doesn't tell us whose face.)

2. Me lavo la cara. = I wash my face.

But if I say "Lavo mi cara", is it grammatically acceptable?

Or do I have to say "Me lavo mi cara"?