I had similar problems on my iPhone 7 when I upgraded to iOS 11. This included apps totally freezing, sometimes for what felt like a minute, with very laggy input, as well as other issues, like not displaying the playing podcast controls for Overcast on the lock screen or in control center. Yesterday I did a fresh install of iOS 11 and then restored from a backup and my problems seem to have gone away. At least for me, it seems like there may have been something wrong with the over-the-air upgrade process. Perhaps this will help you.