My doctor prescribed medicine for me that wasn't covered by my insurance.
My doctor wrote me a prescription that's not covered by my insurance.
この場合、次のような言い方ができますよ。
ーMy doctor prescribed medicine for me that wasn't covered by my insurance.
「医者に保険適用外の薬を処方してもらった」
to prescribe で「処方する」
covered by one's insurance で「保険で適用される」
ーMy doctor wrote me a prescription that's not covered by my insurance.
「医者は保険適用外の処方箋を書いた」
prescription で「処方箋」
ご参考まで！
カナダ 
