Sorry for my confusion. You said, "What happens is that at some point, when I click on a program, it will think as if I have the pointer pointed onto that program." Which program were you clicking on in your picture? Was it Firefox or something else? If Firefox then I think that's a normal display to see the tooltip appear. You could try changing the "mouse hover time" to see if that makes any difference. Mouse Hover Time - Change
This method contains steps that tell you how to modify the registry. However, serious problems might occur if you modify the registry incorrectly. Therefore, make sure that you follow these steps carefully. For added protection, back up the registry before you modify it. The easiest way is to create a new system restore point before editing the registry.
This previous Forum thread may also provide some help: Removing/Delaying Tooltips
There's another tooltip setting called AutoPopDelay. This is set to a default value of 5000 milliseconds (5 seconds) and that's how long the tooltip stays displayed. This is what I could find on changing the AutoPopDelay setting: ToolTip.AutoPopDelay Property (System.Windows.Forms)
But if you were clicking on some other program (not Firefox) and the Mozilla Firefox tooltip appeared, another possibility (since you say this happens after using your laptop for many hours) is overheating. Make sure your laptop's vents are free from dust build up and nothing is obstructing the airflow. Make sure your laptop is on a firm surface and not a pillow, bedspread, or even your lap. A cooling pad may help to lower temperatures.