She cannot speak clearly which is one of the side effects from the medicine she's taking, so she speaks with a drawl.
ーShe cannot speak clearly which is one of the side effects from the medicine she's taking, so she speaks with a drawl.
「彼女は薬の副作用でろれつが回らず、ゆっくりと話す」
cannot speak clearly で「はっきり話せない・ろれつが回らない」
side effects で「副作用」
to speak with a drawl で「ゆっくり話す・ものうげに話す」
drawl は「ゆっくり話す」ことを言えますが、通常アメリカ南部の人が母音を引き延ばす南部訛りの話し方をを指すことが多いです。
ご参考まで！
カナダ 
