Maybe try wearing some floral keds or something like that? It'll take the focus away from how short it is and make it look cute and casual.
I have the exact same romper and going through the same problem! Its really short eh?
Get a short black skirt to wear over the bottom portion to give the allusion its longer. They also sell summer sheer pantyhose that are actually cool to wear. My wife likes them because you dont stick to anything if in a dress, skirt, or shorts. May want to throw on a sheer shell over so you can keep arms meaning shoulders covered
I really don't think you could do anything to make it longer. Leggings would look horrible. For shoes I would wear some stripy sandals.
It may be too hot but you can wear black leggings underneath. I guess it depends on the day outside. Or you can wear a cute pair of Jean shorts just so they are long enough for school. That would make it more of longer shirt with shorts kinda look. Or you can wear black spandex underneath (I recommend that). For shoes, converse would be nice for that sporting/dressy look when you combine them but I would go with white/bage flats.