Acutely tells us that a feeling or a noticing is very strong, not mild. If you are acutely aware of something, you cannot miss it; it sits right in front of your mind. If something is acutely embarrassing, the embarrassment is sharp. The word often goes with aware, conscious, sensitive, embarrassing, or painful. It sounds a little more careful than very or really, and you meet it in writing and in grown-up talk more than in the playground. Though actually, acute also has a doctor’s meaning — an acute illness comes on fast and strong, not a long slow one — so acutely ill is that medical use, not “noticing strongly.” Students mix those two. In everyday chat, very does the same job for feelings; acutely is the sharper, more formal cousin, and it is not a fancy stamp you can put in front of every adjective.