The situation that you described does sound like depression, yes. Thankfully, not severe! Now is really a good time to reach out for help, before things feel worse to you. I think that an anti-depressant would help you gain a little more energy and stability.

Gaining those 2 things would help you feel better emotionally. You could make an appointment withy your doctor, and then let work know that you aren't available to work on that day & time. That's an option too ~ as fitting into doctor's schedules can be tricky, we need to be a little flexible with availability. You deserve that to get the help that you need too!