Since it has been more than two days, know that the problem cannot get better on its own, but it also can get no worse on it's own. Do not plug your phone into a charger before the phone is cleaned inside.
1. Most water you encounter throughout the day contains various dissolved minerals. Even after the water dries, these mineral deposit can remain, bridging one or more microscopic parts which should never be connected. This is a short-circuit. The only way to remove surface mineral deposits is to open the device and clean it physically (scrubbing) or with chemicals that will help dissolve the minerals again.
Dried rice does not accomplish this. If anyone ever insists that you can effectively repair a phone with dried rice, you should turn around and insist that they can clean their kitchen and bathroom effectively with dried rice too!
2. Another issue your phone may have is severe corrosion. Water inside your phone will cause iron and copper parts to rust. As the metals rust they will expand, flake off like dried skin, and then may be deposited where they don'y belong, causing more short circuits.
3. In some cases, functional components may rust away to the point where they fail to work anymore. Imagine a wooden chair with four legs. Termites start eating the chair. It still functions as a chair at first, but eventually when 1 or more more legs get eaten through entirely, you need a new chair. The hundreds of resistors, capacitors, diodes and chips on your phone's motherboard are attached by little legs (or balls) just like a chair. Any of these components that have their legs eaten away will stop functioning, and your phone may not turn on without them.
4. Any phone that has gotten water inside will have problems 1-3, at least to some degree, within minutes-to-hours of getting wet. However the fourth issue is typically caused by the owner: burned components. A short circuit means that electricity will go where it should not go. Plugging in a water-damaged phone before it has been cleaned can cause a lot of power to pass through small, weak components that cannot handle it. Picture the same wooden chair with an elephant trying to sit on it. The elephant is now a greater problem than the termite.
The good news is that problems 1 and 2 your can possibly fix yourself. Ifixit has so many detailed guides that can teach you how to disassemble your device. There's also a good chance your local electronics store sells some of the specialty screwdrivers you may need to open it. If you remove your phone's motherboard and carefully scrub it with alcohol, then soak it for awhile in alcohol, there is a chance you will remove the mineral deposits causing a short-circuit. I would recommend trying this if you are looking to save time and money. However, if your primary goal is recover lost information from the phone, you should bring it to a qualified repair shop first.