It seems like he was barking and barking at the vet's, that's why he lost his voice.
He just kept barking the whole time he was at the vet's, that's why he's hoarse now.
ーIt seems like he was barking and barking at the vet's, that's why he lost his voice.
「獣医でずっと鳴き続けてたみたいで声が出なくなっていた」
to lose one's voice で「声が出なくなる」
ーHe just kept barking the whole time he was at the vet's, that's why he's hoarse now.
「動物病院にいた間中鳴き続けていたので、声がかれた」
hoarse「声がかすれた」を使っても表現できます。
ご参考まで!