Usually I would recommend a restore back to iOS 6, but I'm not sure whether there are blobs available for your device saved that would allow you to. iOS 7 on the 4 is visibly laggier than iOS 5 and 6, so for the 4, I would advise against it for a lot of users.
If anything, plug your device into your computer, create a backup of your device, then manually delete everything via iTunes. Delete all your music on your device, all the photos on your device, all the videos on your device, all the apps on your device, etc. Then on your device, delete all your texts. (Don't worry, you'll get them all back since you backed them up).
Then go to Settings > General > Reset > Erase All Content and Settings. You can say that it's redundant of what you just did, but the reason you'd want to manually erase as much as you can is so that the process doesn't take as long. The process can take anywhere from 30 seconds to a day depending on how much data is on your device. So by removing as much as you can after backing up, you speed up the process.
After all contents and settings are erased, restore the backup using iTunes that you just made previously. See if this fixes the issue. If not, then I'm afraid you might have to upgrade to the fruity-looking iOS 7 to fix the issue