Everybody hates rejection, but I think it's worth trying to build it into your reasonable expectations when pitching music. I've had music published for tv/ media usage (not songs mind - which are a different beast I think) and it was sheer persistence that paid off. If I'd thrown the towel in after the first round of rejections (like I did the first time I tried getting into production music many years ago) I would still be empty handed. I made lots of phone calls, built a database of companies with contact names, email addresses, direct phone numbers and systematically called them asking for consent to submit music. I made sure to ask how they wanted it submitted, and made a note to make a follow up call/ email in 4 weeks if I'd heard nothing.
As it happened, the music I was pitching wasn't picked up, but one of the production assistants liked it enough that he asked me to write something for a brief, which I did, and of the 2 pieces I submitted, one was picked up. Since then I've had a couple more pieces accepted, but it's slow going while you're unknown and unconnected, and I'm sure part of the reason I'm having difficulty is that my production chops aren't quite up to scratch yet. They're close, but only just close enough. I'm *hoping* a concerted effort on that front will yield better results next time I do this.
One last thing: yes, the rejection hurt. And the submissions process was long, boring and very time consuming. I'd have much rather been making music instead...