I find it a tad hard to believe that EVERY single teacher at your school might be busy all the time. You say your dad informed "your" teacher, so that is just 1 teacher, right? I am sure at some point of time you thought that, "I am going to ask THIS teacher to write my recomm". Go talk to that teacher. I am sure there are some teachers that will support you, you must have a favourite teacher. Go ask her! Moreover, those Study Abroad Companies won't write your recomm or send your transcript, so you have to convince your school. Consider talking to your principal.