Funny spots on laptop?

Recently weird white spots surrounded by small red dots appeared on my laptop.

Who can tell me what that could be and whether I can fix it myself or send the laptop in.

You can't fix that yourself. Is damage to the monitor. Either guarantee and you get a new device or you have to live with it or buy a new computer

Do you know how that can happen?

Is mostly a hardware failure. But it may also be that the graphics driver is not correct. You should reload the driver. Or reset the device to the factory settings