The issue was resolved for me when I Restored the iPhone software, nothing else fixed it.
Make sure you have a few hours free, and you know all your logins for your Apple account, email accounts and apps... because this will wipe the phone and you will have to then add all your login details, email accounts and apps (you can select which apps you want to add back on via iTunes).
So when you are ready connect the phone to your computer, select the phone in iTunes, back-up to icloud or your computer. Then choose restore. Then setup the phone as a 'new phone' rather than migrating the data back onto it. Its a tedious process but the phone is running fast now, so worthwhile.
Actually I have had similar problems after migrating to new Apple computers - and having to start with a clean sheet and move stuff over individually, I think after a while things get in a tangle - so best to start a fresh!