This can be different in different schools. So, go to the registrar's office at your school and talk to them. It might be already too late to drop a course which started about a month back but still you should be able to do it. The only thing is that its likely it will appear in your transcript as "dropped".
On the other hand, you should be able to register for your classes which start in March. But again, the best thing is to talk to the people at your registrar's office. This is not a question about H1B or F1 which are general. This is specific to your school and you have to address it through right channels. But, as long as you have 12 credits in a semester, you should be fine with the status thing.