My most recent Carrington ancestor was Mary CARRINGTON (died after 1748), daughter of James (b abt 1661 Chapel-en-le-Frith, d 1736) and his wife Ellen BENNETT (d bef 1737).
I don't know how my Carringtons relate to your Betty CARRINGTON (b 1798 Chapel-en-le-Frith) but know that this Betty had a brother Thomas (chr 5 Jan 1796 Chapel-en-le-Frith) who married Mary SMITH (b 1799 Combs) who I have tenuous links with through her mother Mary FRITH (chr 15 Feb 1778 Glossop)...
I'd be interested in the ancestry of Betty CARRINGTON (1798)