Hi Susan,
The screens on iPads are glued down pretty well and the adhesive doesn't usually fail so chances are something on the inside is pushing on the screen forcing it up away from the chassis. The only thing inside the iPad that can possibly do that is the battery.
Lithium ion batteries as they age can generate gasses that will expand the covering that surrounds them like blowing up a balloon. When that happens the battery is in dire need of replacement. Whatever you do, don't puncture the covering to let the gas out!
There's a Wiki here on iFixit explaining all about swollen batteries that you should take a look at.
[[What to do with a swollen battery|What to do with a swollen battery - iFixit|new_window=true]]
You should definitely open up your iPad and check it. If the battery is indeed swollen, follow the battery replacement guide to remove the old battery, keeping in mind the special preparations and procedures outlined in the swollen battery Wiki.
[guide|16463|iPad 4 CDMA Battery Replacement - iFixit Repair Guide|new_window=true]
You can even order a new battery, with or without the tools needed, right here in iFixit.
[product|IF116-001-4|iPad 3/4 Battery - iFixit Store|new_window=true]
Best of luck with your repair!