I kept bugging my boyfriend to take me to the amusement park until he finally took me.
I drove my boyfriend crazy asking him to take me to the amusement park until he finally gave in.
この場合の「わがままを言う」は次のように言うと自然で良いと思います。
ーI kept bugging my boyfriend to take me to the amusement park until he finally took me.
「彼氏にわがままを言って遊園地に連れて行ってもらった」
to keep bugging my boyfriend until he finally ... で「彼氏にわがままを言う」と表現できます。
ーI drove my boyfriend crazy asking him to take me to the amusement park until he finally gave in.
「彼氏にわがままを言って遊園地に連れて行ってもらった」
to drive my boyfriend crazy until he finally ... でも「彼氏にわがままを言う」を表現できます。
to drive someone crazy で「人を苛立たせる」
to give in で「折れて人に従う」
ご参考まで！
カナダ 
