Unresponsive iPhone 6. Need Notes and Messages.

I got my first iPhone 6 on Christmas of 2014. In February, it starting crashing along with other issues, so i had it replaced under AppleCare. I started restoring the new phone from iCloud the day I got it, February 21st. It never finished restoring (which could be part of my current issue.) This iPhone has been about 90% unresponsive for almost a week (starting March 27th) in that the screen switches between completely black and black with the Apple symbol as if it were turning on or restarting. I can get it to turn off and I can get it to connect to iTunes, giving me the option to either update or restore it. I attempted to update it, but I do not believe it worked (so it's likely on 9.3 instead of 9.3.1.) I would choose to restore it if the device had finished restoring from iCloud when I could use it, but since it didn't, my most recent iCloud backup is from the night of February 20th. I'd rather not lose the past 6 weeks of information on the phone. Out of everything, the only things I really want are my text/iMessages and Notes. I am currently using an iPhone 5 on the same iCloud/Apple ID. If anyone knows of a way I could retrieve these things using iCloud.com, the iPhone 5, or iTunes, it would be greatly appreciated!

P.S. I do have a Genius Bar appointment 2 days from now, April 3rd, but I'd rather get everything I can possibly do done before then just in case all I need to do is restore through my iTunes.