I don't have my homework, my watch today and my watch now. I'm sorry

I am not on duty today.

Sorry, I don't have my watch with me now.

I see you asked whether you took it or not:

Have not taken is the perfect tense. If I don't have my watch, it means I haven't brought my watch yet, which is a strange feeling to use. If I don't have my watch, it is the simple past tense, which should be the time before you say this sentence now, and you can't follow today/now, otherwise it is a tense error.