There's nothing wrong with her voice; don't worry.

The translated word in question is 歌い直す utai-naosu, which actually means "to re-sing", not "to heal [my] voice".

で、なんかとっても私のなかで存在感のある曲だから、あの頃の自分の声でのイメージが強すぎて。今の自分で 歌い直すとなると、なかなかこれがまた難しくて。。。

So, since the song is such a major part of me, my voice from back then gives off such a strong strong mental picture of who I was back then. Now that it's up to me to re-sing it as I am now, I'm finding it really difficult to do again.

In other words, because the song has always been so meaningful to her, she is finding it difficult to go and delve back into it. It is unclear whether she means that it is emotionally difficult to put herself back in the shoes of her 1999-self, or whether she means that it is artistically difficult to find a new way to sing the song while still honoring the original vocals. My guess is both.