The next day after I've had too much to drink, I can still feel the alcohol in my body, so I feel pretty rough.
この場合、次のような言い方ができますよ。
ーThe next day after I've had too much to drink, I can still feel the alcohol in my body, so I feel pretty rough.
「飲み過ぎた次の日は、お酒が体に残っている感じがしてきつい」
to have too much to drink で「飲みすぎる」
to feel the alcohol in one's body で「お酒が体に残っている感じがする」
ご参考まで!