Hello,
yes you can express it that way "he estado muy ocupado con la escuela", whenever the conversational partner knows you are a student (and not a teacher, for example, or a painter who's painting the school facade). Otherwise, you should make clearer what kind of task you've been busy with, for example: "he estado muy ocupado estudiando para los exámenes/haciendo deberes/preparando tareas para la escuela", and so on.
Regarding the second part of your question, you can use "por eso": "he estado muy ocupado con tareas de la escuela, por eso no he podido estudiar español durante dos días", but you could even use just "y", which is the common way to express it orally: "he estado muy ocupado... y no he podido estudiar español". Depending on the CONTEXT, therefore could also be translated as "por tanto" (more formal) or even "luego", as in: Pienso, luego existo: I think, therefore I am.