When I left w*!k, I was covered until the end of the month. I would check when your insurance ends, not your employer's books.
I think the exchange insurances start at the beginning of a month, but with a life event you can sign up +/-60 days of the event. I don't know about off exchange.
If you want cobra and you are right that employment ends, you should have 60 days after your last day to get COBRA.
For COBRA-- talk to your employer's HR dept... they should be able to tell you cost, timing, etc.
“Remember where you came from, where you're going, and why you created this mess you got yourself into in the first place.”
― Richard Bach, Illusions