I know the uncomfortable feeling, but think of it this way. You aren't asking someone for a job. You are asking someone to help you get an interivew. You are responsible for getting the job. Most of my jobs have been because of someone I know. Your instructors are great resource. At least in my program, most of the faculty also worked in a local hospital even if it was 1-2 days per month. They have the pulse of the hospitals.