How to unlock Iphone after it says Connect To Itunes without restoring?

I accidentally forgot my password to my iphone, i just changed the password a few days ago. I want to have my iphone back, but i don't want to lose all of my data.(I have lots) i've looked online that you must be connected to the same computer as when you first synced your device, but i don't have access to that computer anymore. When i tried to connect my phone to itunes on my laptop that i'm using right now, it said, " can't allow access to iphone -- must be unlocked" the problem is, i can't unlock it because its telling me to connect to itunes to fix it --- I'm so confused and angry please help me here

Well it's locked so you can't access anything of course. But when syncing an iDevice to a computer you must do it on the same computer or you'll lose data. Because you must have the data on the iDevice on the computer. The only thing that may work is you may luck out, when a device is synced it first will back up the device and it should ask you a variety of questions including what library to sync to and it should download anything but the music and maybe like files on the device directly to the iTunes and your iTunes account if your logged into your iTunes when you sync it. Also it will backup the iPhone as I said so if you have notes and passwords and other simple data on the phone it should be stored in the backup, almost everything to the wallpaper and specific order of apps you had on your iPhone. In the future I recommend iCloud. Then you can restore from the iCloud all music contacts apps, notes, files and more!