Problems with camera on iPhone 5c?

I recently bought an iPhone 5c (two weeks ago) and it will not let me take more than 70 photos, which is annoying as I bought it mostly for the camera. My first thought was a storage issue, but I have no games downloaded, only social media apps- facebook, pintrest, tumblr, snap chat etc (12 in total) and I've only downloaded about a quarter of my itunes.

It is connected to the itunes on my laptop, and also to my iPad through iCloud- is that an issue?

Maybe your iCloud is full and that is why it won't let you take any more photos.

Thank you, sounds like the most likely reason but I have no idea how to sort that out!