Looking on the Ancestry site, Thomas appears in 2 public family trees (McAlister & Lynch). In both, his place of birth is given as Larne. No source is supplied for that information.
Statutory registration of births didn?t start in Ireland till 1864; registration of non RC marriages started in April 1845. So both the parents marriage and Thomas?s birth are too early to be in the statutory records. You therefore need to rely on church records, not all of which have survived and not all of which are on-line. If you don?t know where he was born, it?s a bit of a needle in a haystack. Caldwell (and the variant Calwell) is fairly widespread in Co Antrim, being a common Scottish name.
If you have no other clues, you could search the church records for Larne around 1841 for Thomas?s birth. You need to know his denomination but I?d hazard a guess that it was either Presbyterian or possibly Church of Ireland. There are 2 Presbyterian churches with records for that period in Larne, and the Church of Ireland also has relevant records. Copies are held in PRONI (the Public record Office) in Belfast but are not on-line and so a personal visit is required to access them.
N.S.P. Larne and Kilwaughter Baptisms, 1720-69, 1796, 1801-03 and 1826-1929; marriages, 1721-69 and 1826-1908; session minutes, 1720-48, 1800-01 and 1828-30; session and committee minutes, 1864-1929; discipline cases, 1721-49; poor accounts, 1720-57.
P. 1st Larne Baptisms, 1813 and 1824-1902; marriages, 1846-1902; marriage notices, 1946-57.
C.I. Inver and Larne (Connor diocese) Baptisms, 1806-71; marriages, 1817-20 and 1826-45; burials, 1826-1905; vestry minutes, 1763-1870; cess applotment book, 1833.
Though most of the Irish censuses pre 1901 were destroyed, a few fragments have survived. Part of the census for Larne and adjacent areas for 1851 is amongst the survivors. So I looked for any Caldwell families in it:
I found two, both with Thomases (one of which was much too old) and in both cases the parents names are wrong.
Z56 LARNE OLD TOWN ST TOWNLAND
WILLIAM CALWELL /HEAD/M/49//GROCER/LARNE/ANT/
JANE CALWELL /WIFE/M//44/NONE/LARNE/ANT/
ANN CALWELL /DAUGHTER/U//18/DRESSMAKER/LARNE/ANT/
HUGH CALWELL /SON/U/13//AT SCHOOL/LARNE/ANT/
THOMAS CALWELL /SON/U/11//AT SCHOOL/LARNE/ANT/
ROBERT CALWELL /SON/U/9//AT SCHOOL/LARNE/ANT/
ARCHIBALD CALWELL /SON/U/7//AT SCHOOL/LARNE/ANT/
GEORGE CALWELL /SON/U/4//AT SCHOOL/LARNE/ANT/
Z15 CRAIGINORNE TOWNLAND
WILLIAM CALDWELL /HEAD/M/76//FARMER/ANT/
MARGARET CALDWELL /WIFE/W//75/SPIN FLAX/ANT/
HUGH CALDWELL /SON/U/47//FARMER/ANT/
THOMAS CALDWELL /SON/U/37//PLOUGHMAN/ANT/
ROBERT CALDWELL /SON/U/35//SHOEMAKER/ANT/
AGNES COLEMAN /SERVANT/U//44/SERVANT/ANT/
SAMUEL CALDWELL /GRANDSON/U/8//AT SCHOOL/ANT/
http://homepage.ntlworld.com/derek.hawthorne/Antrim5109.html
So probably next step would be to get someone to search the church records for you.