How do I backup my iPhone to iCloud?

I've done it before on my old phone but now I want to do it on my 5s. I want to save my iMessages, photos, emails and notes. It shows memory on my iCloud has been taken up from my last phone, but I have 7 gigs more of photos that obviously aren't in the iCloud. I bought the extra 50 gigs. I don't have a computer or another phone. I keep trying to update my backup but it keeps saying could not be completed. People are saying I have to delete my old backup but I don't want to lose that stuff. How do I update it with all my new stuff? Also will there be a way to look at all those picture without having to put them on my new phone. Than

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