How do save photos via internet on iPhone?

So I'm looking for an app that I and use to save photos on (with an iPhone) have around 1500 pics on my phone and only 16gb storage, and it isn't enough anymore. I realize that I can just connect it to iTunes and save the photos to my computer, except I want to be able to have the pics available to me when I don't have access to the computer, if I want to use one as a backround or to edit or something. Also I need it to connect to internet so if my phone crashes I won't loose everything! Something like Instagram ( I don't care if its social media) except without it cropping the photo!

Box, dropbox, icloud…

Apple has the biggest app store on any mobile platform, I'm sure not all if them are useless, find something that works for you… My favorite are the 3 above choices, but their are thousands more

There are several online storage options available. Box & Dropbox are 2 of the more popular ones. Check them out.