While one of the two main usages/meanings of (으)ㄹ까요 is "Shall I/we V", we don't really say "shall" much in modern American English last time I checked ㅎㅎ So I would say that "Should I go to school?" and "Shall I go to school?" have the same meaning. Of course, "Should I go to school?" could also have the meaning of "Do I have to go to school?" In English, we use various words to convey our meaning. In Korean, we use grammar to convey nuances in meaning. So it depends on what you meant by "Should I". That is how you to determine which grammar point to use.