「よくなるにはこの薬全部飲まないとね」看護師は言った。

English Translation

“You have to take all this medicine to get better,” said the nurse.

You need と between 飲まないとね」and 看護師.

FYI: We used to call a nurse 看護婦(かんごふ), but 婦 means female only. So we prefer 看護師 as a gender free term.