I was prescribed some Chinese medicine as well as antibiotics in order to stop my coughs.
I couldn't stop coughing, I got some Chinese medicine and antibiotics at the hospital.
ご質問ありがとうございます。
① "I was prescribed some Chinese medicine as well as antibiotics"＝「漢方薬や抗生物質を私は処方してもらいました」
"in order to stop my coughs."=「咳を止めるために。」
② "I couldn't stop coughing,"＝「咳が止まらないので」
" I got some Chinese medicine and antibiotics at the hospital."＝「漢方薬と抗生物質を病院でもらいました。」
ご参考になると幸いです。
そしてお大事に！
I had a cough for a long time, so the doctor gave me some antibiotics and traditional Chinese herbal medicine to suppress my cough.
この場合、次のような言い方ができますよ。
ーI had a cough for a long time, so the doctor gave me some antibiotics and traditional Chinese herbal medicine to suppress my cough.
「しばらく咳が止まらないので、医師に咳を止めるために抗生物質と漢方を出してもらった」
antibiotics「抗生物質」
traditional Chinese herbal medicine 「漢方薬・漢方医学」
ご参考まで！
アメリカ合衆国 
カナダ 
