Accidents, however small they are, are never fun. They get you thinking about what might have happened if circumstances would have been just a little bit worse than they were and that freaks you out. Plus, no one expects to wind up in an accident, you're just merrily driving in your car, feeling fine and safe and suddenly shit happens.
I'll never forget the day I had my first and so far only accident. I was waiting at a gas station and there was a long line in front of me of drivers all wanting to pump air into their tires with the free-of-charge compressor there and they were all blocking my way out. So, I decided I could back up and leave rather than spend my whole day off waiting for other people. I looked around like I always did, saw nothing, and backed up. Turns out some asshole parked his extremely old, rusty piece of shit right in a place I definetely didn't expect him: behind my car, but way to the right, so that only the left side of his piece of shit was directly behind my car. I hadn't seen him there and well...
Next thing I know I feel a bump and my heart stopped. I had hit his car ever so gently, but enough to make the paint come off my rear bumper, leaving a very nasty area. His car had one or two dents and scratches more that nobody could see among the ones already there. I felt horrible.. I didn't cry, though, being a guy and all that, but I'm so careful with my car that this just freaked me out completely. I was shaking from head to toe and felt completely horrible during the entire rest of the day.
The whole thing ended with my insurance having to pay this asshole almost 300 Euro (which is nearly more than his whole fucking car was worth.) To keep my insurance rates from going up, though, I paid the money back to my insurance company personally. As for my car, me and my father managed to restore the damaged area on the bumper back to near-perfect condition ourselves.
TL;DR: I've been through something similar and know how much it sucks. My sympathies and I'm glad you're alright