I must go to work immdiately after I finish this class.
I gotta go work just after this class.
the first one is formal so you can use to your teachers.
the last one is casual so maybe you should not use to old teachers.
gotta=have got to (in casual way)
I have to go directly to work as soon as we finish this lesson.
この場合、次のような言い方ができますよ。
ーI have to go straight to work after this class.
「この授業の後、仕事に直行しなければいけない」＝「この授業が終わったらすぐに仕事に行かないといけない」
ーI have to go directly to work as soon as we finish this lesson.
「このレッスンが終わり次第、仕事に直行しなければいけない」
ご参考まで！
日本 
カナダ 
