Sounds like a bug it could have is making it go slower I would say try getting a virus protection on your phone, preferably one from your Wireless company.
My iPhone 5s won't let me open text until about after half an hour of use. It's been taking longer lately. What should I do?
By "opening text" do you mean opening a message? Or actually opening iMessages itself.
If you can't open any messages until half an hour after using your phone, then it sounds like an issue with your actual device.
On the other hand, if you're getting a push notification alert about a message, but not seeing the message for a little while, then that sounds more like a problem with your network signal or carrier...
I had this same problem. Try turning your data off and then back on. Also if you have emails automatically updating then that can do it too apparently something to do with how much data I was using...