He/She is full of curiosity and interferes with what I do.
He/She is full of curiosity and interrupts me.
(It is cute though)
「好奇心がいっぱい」は「full of curiosity」と表現できます。
「邪魔をする」はinterfere with somethingとかInterrupt someoneという表現ができますので、
「好奇心がいっぱいで私の邪魔をします」は
He/She is full of curiosity and interrupts me.
He/She is full of curiosity and interferes with what I do.
などと表現できます。
その行動が可愛いなら、It is cute though (かわいいんだけどね)などと付け足すとよいでしょう。