"High" can be used to a refer to a mental state, usually a euphoric one. This can be used to refer to an induced state of euphoria from drugs, but it is also used to describe other natural states of happiness (eg "I'm on a high").
"She's got you high and you don't even know yet"
It is impossible for anyone but the songwriter to say authoritatively what the song lyrics mean, but it seems to me that the song is about someone in relationship with a girl who is making them very happy. The girl may love the person, or they may even be in love but either the person doesn't realise it or is in denial.
"She's got you high" means that the unnamed girl has made the person euphorically happy, maybe that they are even in love; and "You don't even know yet" implies that the person has not yet realised they may be in love, or perhaps just what a good thing this relationship is.
Other lyrics from the song that support this interpretation:
You can't deny you're looking for the sunset
Perhaps this means metaphorically that the person is looking for something beautiful? Again there is a suggestion of being in denial.
It's the search for the time before it leaves without you
Suggesting that if the person doesn't realise this girl is a good thing and respond, she will move on.
What's this about? I figured love would shine through
The writer is saying that love should be obvious, but the person hasn't realised it.
Open your mind, believe it's going to come to
Telling the person in the song that they may be in denial that love will ever come their way, but that this is "closed minded" thinking.
Best Answer
There's a lot of specialist nautical terminology here. I'm not an expert on this, but I've done a bit of checking with people who know more, and I'm reasonably confident.
For a sailing ship to be carrying an environmental condition - sea state, weather, etc - is a term I'm not terribly familiar with, but I gather it just means to be experiencing that condition.
A high sea is referring to the sea state, how rough the sea is.
Being badly pooped is to have a lot of water breaking over the poop deck, or the rearmost, elevated deck on a sailing ship. Even relatively small sailing ships would have this, even if they have no real forecastle to speak of, because it shields the quarterdeck in front of it, where the helmsman (or coxswain) and captain (if they aren't the same person) are, directing the ship.
Now, I tried to find where the dictionaries online might have gotten this quote, and discovered that they missed out a bit of the middle of it that might make it slightly easier to understand, though it's still obscure to the layman:
That makes it more clear what carrying a high sea is meant to mean; on the quarter refers to a direction, between abeam (to one side) and astern. Thus the sea state, the high sea, is being driven from a diagonal direction to one side of and behind the ship. Because of that, there was a lot of water breaking onto the poop deck.