The が should be は
今朝 isn't technically "wrong", but a simple 朝 is more natural here.
I don't think 医者に行く is used very much, usually 病院に行く, although 歯医者に行く is common usage. I sometimes hear 目医者に行く, but can't recall hearing other specialties referred to in this way.
The に after 午後 can be dropped.