Help!!!! iPhone crashed, deleted everything.

I was texting on my phone, when the phone crashed. The Apple sign came up randomly. Then the screen went blue. Then it went into recovery mode. I went restore and update the OS, and all it did was wipe my phone out. I just got a new computer, so I haven't had time to make a back up, but all my important information is still on iCloud.com..... Yet, when I sign in to restore from iCloud, it says there is no back up available.

Backups are EITHER stored locally on your (presumably "old") computer, or in the cloud. Which setting did you have set up? I'm guessing local backup, so your only real hope is to either do a restore from the old machine that still has your backup, or see if you can find the old backups from the Time Machine archives you would have (hopefully) with your new computer.

Even if that doesn't work out, you probably haven't lost much. Your mail is still on iCloud, all your app and iTunes purchases are still backed up there, contacts, calendar and so forth are on your new Mac ... so even if you have to set it up as a new phone, you'll still get most of what's important back ...