Checking my last day of health coverage (update)

I was told my coverage ends on my last day, but the letter says the end of the month. There are 3 people counting on me, so I am trying to be careful. I do not want to be surprised by a bill. What should I do about appointments?

Thanks for writing this out. I went through something close to it last year, and it got easier once I kept a simple log of every call and form.