Wendy, if the Peter to whom you refer is the famous lexicographer Peter O'Connell, then there has been a great deal written by him and about him, in both Irish and English.
The most extensive biography is in:
Ní Dheá, E. (2000). Peadar Ó Conaill, scoláire agus scríobhaí (1755-1826), in C. Ó Murchadha (ed.), County Clare Studies: Essays in Memory of Gerald
O'Connell, Sean Ó Murchadha, Thomas Coffey and Pat Flynn, The Clare Archaeological and Historical Society, pp. 137-149.
Ní Dheá cites `cnuasach ghinealais' written by O'Connell in RIA 23 H 22, which may or may not give details of his own genealogy.
Other sources include:
`Peter O'Connell' by Brother Seán McNamara in Living on the Wild Atlantic Way, 2017, pp. 350-1 (with further sources listed in a footnote on p. 600); `The man who put Tom Moore off history' by Mannix Joyce, Sunday Press, 19 Aug 1962; `Eugene O'Curry and Thomond: II' by Mícheál Ó hAodha, Irish Times, 31 Jul 1962; `Death Sails the Shannon' by W. MacLysaght (The Kerryman Ltd., 1953); Sunday Tribune, 24 Feb 2002; `Peter O'Connell: Scholar and Scribe 1755-1826' by Dermot F. Gleeson in Studies: An Irish Quarterly Review, Vol. 33, No. 131 (Sep., 1944), pp. 342-348 (7 pages), Published by Messenger Publications, available at
https://www.jstor.org/stable/30099510
Also Life Sketch of Peter O'Connell by Michael Twomey at
https://www.duchas.ie/en/cbes/4922318/4869535/4932004
etc. etc.
Unfortunately the various sources sometimes disagree on the details of the O'Connell family.