In the winter of 1820, the New England whaling ship Essex is assaulted by something no one could believe—a whale of mammoth size and will, and an almost human sense of vengeance.
This movie contains 5 potentially triggering events.
I don't know the actual time, but it's a few minutes after they set sail. There's a dinner scene where the character in question is acting sick, so you can prepare for it. After that, he and another character go to the edge of the ship and one hangs the other over the side. After he gets pulled back up, look away and cover your ears for about 30 seconds and you should be good.
There's another scene later on where the same character has to go inside a whale carcass. He gags and wretches a couple of times but doesn't actually get sick.