BIG HELP!!! iPhone 4 Storage and Texts???????

So recently today my iPhone 4 which is running on 6.1.3 has been saying "Storage Almost Full." I am not sure what this means because I have literally deleated tons of stuff on my iPhone. I have a good 3.61 GB free space. Every 5 minutes it pops up saying the same thing.

ALSO****** When I try to text people, the text will show that it is sending, and once it is at the top, the texts itself disappears. The other person doesnt get the message. People try texting me and I don't get the message from them. My brother which is on the same plan is haveing no problem. Please please help with this problem. I also tried deleteing the text "lobby" (I guess you would call it) Text chat thing? And the person would just re-appear in the text section. So it wouldn't go away.

I fully restored it to New iPhone and it still happened, I backed it up, turned it off then on. I have tried everything. PLEASE HELP!!!