Dear Mary
Welcome to Ireland Reaching Out and apologies for the delay in replying to your message.
As you can see from the link below, Hospital is a Civil Parish in Co. Limerick:
http://www.irishtimes.com/ancestor/fuses/townlands/index.cfm?fuseaction=TownlandsInCivil&civilparishid=1569&civilparish=Hospital&citycounty=Limerick
Records for the corresponding Roman Catholic Parish of Hospital and Herberstown begin in 1810 for baptisms and 1812 for marriages. As this is the case, there will be no baptism record for Michael. What you could do is check the sites listed below for other Nealon names. The surname Nealon is not very common and so you could begin an information gathering exercise on the basis that you may be able to link the names at some point in the future, if new sources become available.
www.familysearch.org has a huge database of genealogical records including some church records for Ireland.
www.rootsireland.ie have a large collection of Irish Church records, however you have to pay to use this site.
http://churchrecords.irishgenealogy.ie/churchrecords/ have begun a project to upload Irish church records to their site free of charge. However, so far only Counties Dublin, Kerry, Carlow and parts of Cork have been covered.
Have you tried searching Ancestry.com for any mention of your ancestor?s name in member family trees or messages? There is an extensive Nealon family tree on the site:
http://homepages.rootsweb.ancestry.com/~tdgarner/nealon.htm
I would also suggest you check 'Information Wanted' on the Boston College website on the off-chance other Nealon ancestors travelled to the US: http://infowanted.bc.edu/results/
In relation to the book written by your ancestor, it would be very difficult to ascertain what or where it is or what it contained. It may have been as simple as a pamphlet or a type of flyer or more advanced.
Please let us know if you make any further progress with your search
Best wishes
Clare Doyle
Genealogy Support