Does my iPhone 5S have a virus?

Lately I've noticed multiple problems. Apps spontaneously close, and when I try to open them again, they will seemingly open back up but quit again. Also, I'm totally out of storage, and even if I delete multiple apps and songs, I still have 0 bytes of space. I can't add anymore bookmarks in safari, and when trying to open an attachment I got from a test, the phone vibrated at this weird pattern then vibrated constantly until I exited the chat window where the attachment was and the attachment never opened. Also, sometimes all of my contacts will disappear and all of my previous messages will just have the phone numbers and not the names of the people. But hen I restart my phone, the names come back. Restarting it does temporarily relieve a few problems, but only temporarily. Do I have a virus? What should I do?

It is impossible for an IOS device to get a virus. No vulnerablilites have ever been found in the apple phones but i'm pretty sure its because you are out of storage. When you are out it does that. My iphone 4 did that and it got to a point where i couldn't do anything so I deleted everything and it helped. You should prob delete everything and make a backup for them

When you restart your phone are you doing a real restart -- holding down the Sleep/Wake button and Home button at the same time for about 6 seconds? Doing a real restart has solved similar problems on my iPhone and iPad several times.