I'm almost sure that there's no such option in TW. So if you're not using another launcher another possibility could be this. Go to settings, accessibility, touch & hold delay and make sure it's short. Having it long can cause your problem.
I don't know of any other settings that could do that, just other apps locking the icons.
I assume that you just tried the normal things like soft reboot and battery. Some people recommend wiping the cache partition. Nothing is going to be lost, but I've no idea if that could solve the problem.
You hit the nail on the head! Yes, I had soft started the phone several times, but until you mentioned it, I had not cleaned out my cache in quite a while. I went in and took care of that and now icons move as they ought to. Thank you for such a quick reply and sticking with me through this.