To be/get swept up/away by something is to have a strong emotion, almost always positive, that causes you to not notice or pay attention to anything else. A person can be swept up by excitement, enthusiasm, enjoyment of something. A person can be swept up/away by their feelings for someone else, usually love, "She swept me away," in this case a person can also be swept off their feet.
To be closed up by something means the opposite of causing interest in something and is not common. It is used in your example to contrast with "bring out the best".