I'd throw a cropped denim jacket, a bolero jacket or a cardigan, it'll make it more school-appropriate. Definitely love it as is for happy hour or lunch with the girls.
Nothing is too dressy for school! People need to worry about being too casual! Kid used to wear slippers and sweats when I was in HS and that is not a good look! Care about what you look like, it'll take you far in life
Too dressy is what you make it. If you wanna dress like that ( and I think you should) than go for it. Don't let other peoples opinion of too dressy guide you.