Hi James,
May I please ask if the info we have posted has helped?
You had written that you desperately needed information, and I can see that you have been online several times since each of us has posted, but I cannot see if you have found the info helpful.
I do have many offline NSW resources, particularly for 19th Century NSW and I am happy to look further, but they are hardcopy resources, so they are not keyword searchable.
You were asking about Thomas Young's birthplace and where he was from in the USA... If he was born in the USA, then may I ask HOW LIKELY would it be that he was a British Subject? (It is of course possible, if say his father was British .... )
Cheers, JM