I think all have the same fears after graduation. As for me, I started to apply for a job right after my graduation and I enjoyed it very much even if I am very nervous at the beginning. The only thing that I thought myself while applying is to not expect too much to lessen the agony of failure. If you don't get the job, move on, then go on to the next application, that's how life goes. You'll eventually get one if you persevere.