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The RC parish for the area was Castlebar/Aglish/Ballyhean/Breaghny https://registers.nli.ie/parishes/1039 Castlebar is the main town and the civil parish was Aglish. So it was/is the same parish and in the mid-19th century, there were likely as many as four chapels for the parish. When you look at the index page for the parish register, you will see an annotation saying " The pages are in great disorder" for the baptisms from 1838-1855. I tried to find the record for Bridget and I did not find it but it is clear that there are multiple priests involved and the records around 1844 are not in one numerical sequence by date but we know Bridget's record is there somewhere because it was transcribed by Roots Ireland. Also, Nancy is a variant of Anne so bottom line the two records mentioned are for the same person.
I looked at the 1855/1856 Griffiths Valuation head of household listing for Aglish civil parish and there were two Quigley records for Carrowbrinoge townland so likely Patrick Quigley was from that townland. http://www.failteromhat.com/griffiths/mayo/aglish.htm
Let me know if you need additional assistance
We do not have a parish liaison for the Castlebar area but I will alert our HQ about your March trip.