I don't know if this helps you at all - (it helped me to think of it this way)
a feeling is just an emotion, feeling angry is normal, and helpful in many ways (we'd be abnormal if we never felt angry - ever)
but your question was slightly different - is it OK to BE angry.
a) of course it's Ok, but
b) I don't really like being defined by my feelings - a feeling doesn't have to turn into action and I don't have to BE whatever I am feeling.
I find it exhausting and not particularly helpful to walk around "being" angry, but feeling angry - that's working through an emotion, it's temporary, doesn't define me and helpful.
I found I was much more able to process anger in a useful manner (i.e. not stuff it down/turn it inwards) once I thought of it like this.