Actually, the Japanese text was also wrong, making translation more difficult.
breath for us 感じるたび 胸が熱くなって
知らない自分に
なった気がした
(not なって)だけど、気づいたから ちゃんと、
わかったから (not わかったか)そうだ… これは魔法なんかじゃない
Even though the current translation is much better, some problems still remain:
- 知らない自分 is "myself that I had never known before".
- だけど、気づいたから ちゃんと、わかったから is can be either "however, because I was able to understand it [= my new self] from the very moment I noticed it" or "however, as I noticed it and was able to understand it". However, taking the punctuation into account, the latter is more likely what is meant.