Why is glue coming out of my laptop?

Seeing as you have what appears to be a massive crack in your glass it is entirely possible that this is an optical bonding compound between your screen and the glass leaking out. The crack on your glass layer has probably broken a sealing layer at the edge of your screen.

If your screen is not actually cracked then that line towards the top will be the liquid level as it slowly oozes out of the display panel. The crack may not be in the front glass but instead in the seal that was meant to keep the compound in.

Optical bonding compounds are used to reduce glare and surface reflections in order to improve the look of the screen.

In theory the compound should be harmless, though I wouldn’t go licking my fingers after touching it. I would expect the chemical to be a silicone gel, as described by companies such as Display Technology:

Using the VacuBond®, various components are bonded together with the high-performance silicone Opto a-Gel in a clean room. The optical bonding fills the air gaps between the individual components and reduces the reflection of light on the surfaces by 99 percent! So the readability of our TFT displays is excellent, with perfect contrast and colour brilliance.

Chances are the chemical will slowly leak out from between your glass and TFT over time, with bubbles forming and making it appear that it is leaking “into” your screen while it is actually leaking from it.

Your best option for a permanent fix is to replace your display assembly.

If it were from the TFT itself I would expect to see a more significant “damaged pixel” look to the display, such as can been seen in the image below from the question What are these LCD defects if not dead pixels?

I would also not expect the quantity you describe cleaning off daily if the TFT liquid crystal layer were leaking. That layer leaking would definitely be more of a health hazard.