I just had this same exact experience with an iPhone 7 Plus. After figuring out that it would boot with the selfie flex cable unplugged but not when it was plugged in I decided to take a closer look at the selfie flex cable. The tape on the bottom of the selfie cam flex cable that covers the connection points was left on the old screen. I noticed the missing tape and realized it had already been stored with the other good LCDs so I cut a piece of black electrical tape and put it over the connection points. Now the phone boots up just fine.
Once a phone gets wet we focus on saving the data and not saving the device. Too many things can still fail on the phone after a liquid damage repair is done. Because of that we focus on saving the data on the phone. We will first take the logic board out of the phone and put it through an Ultrasonic Bath which makes connections work again that would not work for any other reason. We will then inspect the board under a microscope looking for burns or obvious problems. We then find those problem components on the schematic to learn what that component does. Then we carefully heat and remove the old components and clean the area to get it ready to take the new component. We will solder the components into place in order to get the phone to give up its data. Often we can get the phone working just long enough to grab the data or make a backup. It is a pretty difficult repair and it is not always successful.
I agree with Chloe that a new screen will most likely fix your problem. If a new screen does not fix the glitching then that will tell you that the logic board has an issue. Sometimes after a hard drop a cold solder joint can form behind the Touch IC which would cause glitching like you describe. Good luck.
If it is an RCA then chances are you can replace it for less money than it would cost to repair it. You can take it for a professional repair which means they would take the logic board out and put it through a Ultrasonic Bath and then inspect it under a microscope looking for burns or obvious problems. Some microsoldering may be required if burned components are found. This type of repair takes a highly skilled tech and the cost is usually pretty costly. My shop will only take liquid damaged devices in for repair if the data on the device is what they want to save. We dont repair the device for the devices sake.
It is often just an alignment issue when the proximity sensor doesnt work after a screen replacement. You will need to open it up and look closely for the plastic brackets that guide the sensor and camera into place. Sometimes the tiny clear plastic part comes from from the old screen sticking to the sensor. Then if the new screen already has a bracket you would not be able to line it up right. If you checked and the old bracket didn't stick and move over just press down on the back of the sensor when it is perfectly lined up and feel for the click when you finally get to fall into place. Often this will fix the problem but you should keep some extra proximity sensors and front facing cameras in stock for when this happens.