Baby delivery in another hospital

I’m pregnant and due very soon. When my labor starts, can I just arrive to Alexandra Cohen hospital even if my OB is affiliated with Mount Sinai? Will they refuse me?

I really don’t like my OB but it’s too late for me to transfer to Weill Cornell (OBs there don’t accept transfers after 20 weeks). I was hoping I could at least give birth at my preferred hospital with the best facilities and doctors on call.

I’m so sad and blaming myself for not switching OBs earlier, but I was battling hyperemesis and demanding work…

Or maybe you have any other suggestions for an OB in NYC that might accept transfers?