Pretty much all the Irish Catholic parish records are now available online on Ancestry, Findmypast, and Rootsireland and the transcriptions are linked to images of the original register. The transcriptions are not perfect so sometimes you might have to be a bit creative with your search. As far as I know Findmypast (and possibly Ancestry) allow access to these records without a paid subscription, Rootsireland requires a paid subscription.
As for proving whether a particular record relates to your family, that can be very difficult especially with common names. My approach is to try to find as much information about each individual and family - both the ones you know are connected and the ones you are trying to link and look at every detail on any records you can find. If you are lucky you may come across additional clues that help to establish the link. You can also try to eliminate potentials eg. look for marriages of Margaret in Monasterboice, if you find one and her father is Michael then the Margaret baptised in 1844 is probably not yours.