Does alcohol make you feel more depressed the next day after drinking?

Yes. Alcohol is a central nervous system depressant. If you are depressed, you should abstain from alcohol. I see no benefit coming from it's use. If you are depressed and not under treatment, please a mental health provider and get an evaluaiton and please stop th alcohol for now.
Most of the time. Yes, most of the time, unless you drink very occasionally and in moderation.