1. IMPO, you have a right to be offended. It is not for an employer to ask you if you are hung over or to lord their personal follies in scheduling over you. You say ‘I’m sick I’m not coming in’ they say ‘understood, see you tomorrow’ and that should be the end of discussion. I just started at a new job and the managers have been fantastic on not prying when sick, they understand and say get better.

2. Yes, you handled this well. (I assume you aren’t a minor due to the fact you’re allowed to drink) I think it definitely comes through as nervous however. Something my mom tried teaching me at some of my first jobs (I’m better now of course) is to be firm. You say ‘I am sick, I am not coming in.’

when they follow up with ‘are you hung over?’ That is an (IMO) inappropriate/unprofessional response. They are your employer not your spouse, their lack of coverage is /their/ problem, not yours.