If you can't handle rejection then this business is not for you. As a musician I had dozens, and I put out far more proposals for audio post work than I contract for. An actor will get one part for every fifty auditions. I have a friend who's a writer; he has a pile of rejection slips literally three inches thick.
The entertainment industry is all about rejection. There are tens of thousands who want to participate, hundreds actually do, and only a few dozen become enormously successful. I'm happy with just being able to make a living, and it took a long hard road to get here.
So either put up or get out. Harsh words, I know, but it's a harsh business.