Brownshiel doesn't appear on my map although there is a Brothershields B. (Burn?) which flows into the River Tyne which goes through Haddington. ... and there is a Blackshields. It does seem this may be a farm. I had hoped someone at present in the area would appear to help you. Maybe if you provided more data we could say where to look next. ( I say we because I'm sure someone out there knows more). Meantime I'll try my nephew - too busy for genealogy - but he lives in Haddington and may know. Jim McArthur