Sounds like what is known as "ghost" touches to the screen. This indicates that the screen is defective and needs to be replaced on your iPhone.
Make an appointment at the Apple Store or take the phone to an authorized Apple service shop to let them test and confirm. Estimated cost of a replacement screen $150 for the iPhone SE.
You can find a list of authorized shops in your area by using this link: Find Locations
When the repair is complete, you will start all over again with a new setup of the phone. Hopefully, you have a recent backup that you can use to restore data back to the repaired phone.