I had this problem once. Here are two things I tried -- eventually it worked again.
1. Turn off Wi-Fi, Bluetooth, Cellular data. Wait a bit. Do #2 before turning back on.
2. Reset the phone. (Hold down power and big button until you see Apple logo.)
Hope this helps.
Texts(blue) not going through,
These are not texts, but iMessages. They go thru Apple servers, not Verizon servers. Do what has been suggested, but iMessages not going through can also be a problem where the person you are sending to recently switched from an iPhone to something other than an iPhone without first disabling iMessage properly. In this case, the problem lies in that your phone still thinks the contact has an iPhone but since they don't there is no way for them to receive that iMessage and your phone would register the message as having failed. The contact would have to properly disable iMessage on their AppleID account before you would be able to send them text messages without having to let the iMessage first fail and then resend as a text.