Repeated Storage Almost Full Error

I am having a persistent repeated storage almost full error. I deleted almost all my larger apps and many of my pictures and videos. Today I deleted another app and the phone said I had 480 MB free. A half hour later it was saying I had 0 kb again even though I didn't add anything to the phone in the meantime. I plugged it in to iTunes and iTunes is saying I have plenty of space on the phone.

Apps are crashing regularly.