Don't let it come to your head.(それを頭にこさせるな)
Don't be (so) conceited.(そんなに思い上がるな、うぬぼれるな)
Don't be (so) sure of yourself.(自分を過信するな)
Don't flatter yourself (too much).(自分をあまりほめ称えるな)
Don't think (too) highly of yourself.(自分のことを過剰評価するな)
Don't think you're perfect.(自分を完璧だと思うな)
などがお勧め。ちなみに「うぬぼれ屋さん」のことは、男性なら“Mr. Perfect”、女性なら“Miss Perfect, Mrs. Perfect, Ms. Perfect”なんて言います。
