Having a part-time job is something that you have generally, not on a particular day. You could also say in your example that you 'have a few hours work today'.

Tip: Use "part-time" with a hyphen when it describes a job. Also, instead of "depressed" (which is a strong word used for serious emotional states), try phrases like "feeling down" or "a bit tired" when talking about everyday moods—they sound more natural in casual conversation.