Check your flex cables for creasing, bends etc. The display cables themselves (as opposed to the stuff from the earpiece assembly) should have a very specific curve to sit properly. I would check the old display, especiailly if it is the original one and try to mimic the shape of those as closely as possible.
They should have no hard folds, and check to make sure there is no exposed copper in the cables. It sounds like something may be inadvertently touching ground, you may even be getting the cables pinched between the display and the housing, I would check to see f the screen is flush on the right side, I used to have issues getting this to sit right when i first started doing iPhone X displays. That curve of the cable needs to be wholly tucked into the phone before it gets closed.
Could also be some of the traces within the cable itself are becoming broken when everything is all squished into the phone, cables on aftermarket screens are generally not as high quality as an OEM on. SIM tray is also right in that vicinity so inserting the sim may move some bits around, or push pins up that are normally lower into the slot.