In English, the sentences "I am scared" and "I am scary" have almost opposite meanings. However, every translator I have seen translates them both the same way: "나는 무서워요". Is there a way to distinguish between them within a sentence, or does it just come from context.
Yes, 무섭다 can mean both "scared" and "scary". Other similar words also behave the same: 재미있다 (interested / interesting), 지루하다 (bored / boring), etc.
Normally, to say "I'm scared." you just have to say "무서워요." There's no reason to add "나는", because who else could it be?
"I'm scary." is more tricky, because if you just say "무서워요", the most natural interpretation is that you're scared. You can paraphrase: "나는 무서운 사람입니다." (I am a scary person.)