Hi Mathew,
"Ghost touches" as the problem you're having is described, is a result of the phone's processor getting bad data from the digitizer, or touch screen. It's usually a result of a damaged touch screen, as there are delicate connections between the flex cable that goes to the logic board and the glass on which the digitizer circuitry is printed. The glass does not have to be cracked for the touch screen to fail; it's frequently the case that no damage is visible at all.
It is possible for the problem to be located on the motherboard, but since those issues are generally not repairable by us normal home DIY-ers, let's stick to the part we can fix, the screen.
The best chance you have to fix this yourself is to replace the screen, but there are certainly things you can do to try and diagnose the problem before you go ahead and order a replacement screen. Unfortunately you'll have to open up the phone to check those things out. You can disconnect the screen connector, clean it with 90% or higher isopropyl alcohol and reseat it firmly. If that doesn't help, then it's probably time to replace the screen. For that some instructions would be nice; unfortunately iFixit doesn't have a guide for you, but there's a German site called iDoc that does.
[link|https://www.idoc.eu/guides/en/samsung/galaxy-a13/replacing-the-screen/954|Samsung Galaxy A13 screen replacement - repair guide|new_window=true]
Good luck; let us know what you find!