Correct. But there is a little more: http://www.gaidhliggachlatha.com/blog-mios-na-gaidhlig/how-to-say-yes-and-no-in-scottish-gaelic
It's easy to see our Irish 'Tá' in 'Tha' but 'chan eil'? Less as much! Maybe it's a longer variant of 'níl'?
For those examples we'd say:
'Tá tuirse orm' or 'Tá mé tuirseach' (I'm tired)
'Níl tuirse orm' or 'níl me tuirseach' (I'm not tired)
Scíth (sgìth) also means tiredness in Irish too, but we don't use it like this! It's used more so to mean rest!
Didnt mean to derail this thread, i just love seeing the similarities between our languages!!