You will want to find a reputable repair shop that does micro-soldering.
You can Google a repair shop locally preferably, but this is a specialized repair and hard to find in most cities.
Luckily, there are several Pros here on Ifixit you can choose from that offer Mail in repairs.
Your Logic board will need proper decontamination / cleaning in an Ultrasonic cleaner with the proper cleaning solution to remove most of the corrosion. It will require removing the several soldered on shields to get to about 80% of the components for cleaning and testing.
Water damaged phones can be properly cleaned and repaired for Data recovery in some cases. The problem is that even with proper cleaning and repair, other issues can eventually arise due to corrosion under components so the phone may not be permanently fixed, but possible to repair just enough for Data recovery and then use the phone until some other problem shows up.
If the tech that already diagnosed shorts on the board has the ability clean the board properly and repair them, Id definitely have him get it cleaned right away to prevent further corrosion. If not, get it to the repair shop that can as soon as you can and do not apply power, charge or try to turn on until it has been cleaned and repaired so you don't cause further damage.
For future water damage on your phones, do not use rice. Get the phone apart ASAP, disconnect battery, keep track of where every screw goes, and soak the board in 99% alcohol for about 10 minutes, swirling and gently scrubbing with a soft toothbrush, cleaning the housing, charging port and everything you can to displace the water and get it to a repair shop right away.
Let me know if you have any questions or need a few suggestions on where you can send your phone for repair if you need it.
Best of luck!