Erased iPhone through first synch/back up mistake. Can I recover data?

I have a new iPhone & been using it, taking photos etc. I then went to synch with iTunes for the first time but when I connected, I accidentally clicked restore as backup from iPhone (which backed it up as my old one!) instead of set up new iphone. It's erased everything i have done on the new phone. i tried one of those data recovery companies but just comes up with the back up stuff. I've lost valued photos, all messages and texts, all my notes. Can I recover them or are they lost forever? Help! Thank you!