One excellent source of information is the Freereg site:
https://www.freereg.org.uk/This has a number of baptisms for Thomas Burge in Frome and the surrounding area.
https://www.freereg.org.uk/search_queries/5e2acc2cf493fd6a19d4ea03?locale=enI did a search for a baptism from 1810-1820. You might consider Stoke Lane as a possibility since this isn't that far from Frome. The only Thomas I can see who has a father by the name of Thomas, is the one baptised on 23/05/1818.
There are two Family Trees for Thomas Burge, b1811, on Ancestry. One has him born Frome and the other states he was born Wales. There are no sources for this information. It appears to be the same Thomas Burge as they both show he died in 1887 in Crawford County, Missouri. They both show his parents as Thomas Burge b1793, d1841, Stalbridge, Dorset and Mary Ann Hellier/Helliar, b1793 Henstridge, Somerset, d1768 Stalbridge, Dorset. They are shown as having had 7 children.
The trees also show the parents of Thomas Burge b1793, to be John Burge, bc1759 Stalbridge, Dorset, d1845, Sturminster, Dorset. Mother as Catherine Thorne b1758 Melcombe Regis, d1823, Stalbridge, Dorset. They are shown as having had 7 children.
The Burge line goes back beyond that to Matthew Burge born c1720, Stalbridge, Dorset.
You would need to check the information on these trees in order to verify it as there aren't sources given for this.
I have Burge in my family tree and they came from Trudoxhill and Nunney which aren't far from Frome.
Jo.