Unfortunately, the NLI page for the Ballingarry parish suggests that there is a gap in baptisms between 1828 and 1849, which is when John and his siblings would have been baptised.
Therefore, I am not sure you can know, with certainty, that John was the son of William White & Anne Shea, because his mother's name was not given on his marriage certificate.
I can see the marriage between William White and Anne Shea (names under their Latin forms) on 21st February 1835 in Ballingarry. However, could there have been more than 1 William White in Ballingarry at this time?
I can see that John did have a daughter called Anne, so I suppose that could be considered supporting evidence.
Unfortunately, it is likely William died before civil registration of deaths, so it may not be possible to find his death date.
However, there is this possible one for Anne:
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1878/020489/7189891.pdfAn Anne White of Knockfierna, aged 75 and widow of a farmer died on 5th December 1878. The informant was a John White, occupier.
This would give Anne an estimated birth year of c.1803.
I can only see Ballingarry baptisms from 1825 onwards (with the gap), so her and William's baptisms are unlikely to be found.
Queenie