Whenever you're dealing with water damage it's always at best a 50/50 chance on getting the device fully restored to its previous condition. There's also a lot of misinformation out there about fixing devices that have been immersed in water. Your first mistake was to fall for the "Rice Trick" method. Your device has many layers in the design. From the back there's a protective casing/frame, cables, a battery, a logic board, camera, speakers, vibration motors, and more. Water is a liquid which is quite handy at getting into the tightest nooks and crannies. Throwing it in a bag or bowl of rice helps only in absorbing the water nearest to any openings on the device but it doesn't really touch or help evaporate the other liquid still within the various layers.
What you're dealing with could (and likely is IMO) related to a faulty display. After water damage I always recommend replacing the battery, charging port and display to begin with. One may reasonably need to replace other components too as they fail but these are usually the main components to start with. But screens can be expensive and you're trying to save on cost. What's going on is you likely have a faulty digitizer or digitizer connections. So let's go the cheap method of troubleshooting. Disassemble the device and take out the logic board. Purchase some Isopropyl Alcohol of at least 91% purity (should be about $3 from Rite-Aid/CVS/Walgreens) and then a soft bristled toothbrush ($.99). Take the alcohol and pour it into a washable clean container and submerge your logic board within the solution for about 30-60 minutes. Longer is better in my experience. Take out the board and use the brush to gently clean all the connections then, once fully dry, reassemble the device and test your screen. If it's functional that may have fixed the problem. If not, your next method of troubleshooting is with a new screen.
*iFixit allows you to purchase a part you may need to fix the repair and, within 30 days, return the part for a refund if it turns out the part doesn't fix the problem you're experiencing.