Perhaps it's on usage, but I feel that 'looking about' is always looking about some thing, usually for extra details or similar. If someone is in a difficult situation and they are looking about, they are looking for the way out of the difficult situation, for example... Looking around is looking for something, generally. A person can be looking around a shop but not really wanting anything so much. Did you submit your answer to see if it'll get accepted? Could take some time.
Not really that concerned about being accepted. After doing exercises until my eyes cross, I start wondering is Duo too narrow in their interpretation, or have I got this all wrong. So I go to discussion for a change of pace and a broader perspective. I see this discussion relatively brief though it is, spans four years so immediate feedback is a rarity. Thanks for your thoughts they give me strength to return to the salt mines.