Hi, welcome to Android forums!
I'm very sorry to hear about your phone! There are a couple possibilities, but they are slim.
If your case manufacturer has a guarantee against damage, you may be able to file a claim with them.
If you have insurance for your phone, also there you could make a claim.
Otherwise it sounds like either repair or replace. You can fine fairly affordable used phones on swappa.com and that is a very safe place to buy compared to ebay or craigslist. I have bought a few there, as well as sod a few. Good place to find affordable replacements. My wife recently left her HTC DNA on top of her car and drove away. We never saw that phone again. Bought a replacement right away. Good as new!
You could look into a local cell repair shop, but see if you can find honest reviews of it before diving in. Maybe get a written estimate which protects the consumer in some states against bait and switch, or over charging.
I personally would just buy a used one. It looks like the cheapest one on swappa right now for ATT SIII is around $270.
Good luck!