Are you at a UK university? We have lecturers rather than teachers, lectures rather than classes, and it would be impossible to have all teaching delivered by a single lecturer for an entire year.
All UK unis have a student counselling/support service. If you're in this country, start with them for advice on how to deal with the situation and maybe for info on where to get practical help with your stutter.
If you're outside the UK it will be very difficult to advise, as this is a culture-type problem which will vary between countries.