That's my point. Of course she was. But she didn't care. That's the purpose of that scene: to show that she is not going to stop, not ever. Come what may. You get in her way, you get cut down.
That's also very much intentional. It's no coincidence Galadriel is often mentioned in comparison to Fëanor. She is his counterpart, all the pride and selfishness that made the Noldor so susceptible to Fëanor's curse, though unlike him she manages to overcome it in the end. She was not a nice person at many times in her life. The Galadriel from LotR is THOUSANDS of years later. It's not how she started. And it's not what she is at the time of this show.
In LotR, which is thousands of years later. It was not the case at this point in time. Galadriel is much older than Elrond. He wasn't born in Valinor, he had never even been there. Elrond did not start out as the ring-bearing lord he is in LotR.
We don't really have books to go by for this. There isn't enough material on Galadriel that covers her actions during this time; in fact she's mostly absent from events as described. However, we know Tolkien planned to change her into more of a warrior type. He talks about his plans in his letters, wishing to expand her into an amazon-like character featured in more stories. He just never got to write them before he died. The show is taking liberties with the character based on that, since there isn't really much actual source material, just snippets here and there.
I'm not too happy with the first 2 either, but to be fair, I also didn't think Sandman was that great until after the 24h diner episode. It really picks up in the second half. I'll give this a bit more time; but not too much more. At least it's not WoT.
It is a bit silly. I'd have just made it so she sees a Númenoran ship in the distance, and that gives her the idea to jump. She swims towards them, gets picked up, and gets shipped straight to Númenor. That whole castaway bullshit with the sea serpent was completely unnecessary and boring.