We have all been there man. I have had similar instances throughout my life. I would cope by becoming completing numb and just locking up my feelings so to speak. However all the feelings would come hit at once it would make me feel like shit. However, one thing that I can assure you of is that with time you'll learn to grow a thick skin. You can obv learn to improve your stutter but you'll realize that it's okay even if you do. Most people I have met at uni or work have been very nice about it. Maybe you can talk to the instructor after class and let him know of your speech impediment. Im sure he'll be very accommodating