There are three main methods you can try to fix a stuck pixel before investigating your warranty: software, pressure, and heat. However, it should be noted that the latter two options have the potential to cause more damage to your machine, so exercising caution is very important. Before you try any of these methods, it's also worth turning off your device for a day or so, which might be enough to reset the pixel.
Fixing a stuck pixel with software
The easiest and safest way to fix a stuck pixel is through software designed to unstick them. If you don't feel like downloading a program for it, JScreenFix is a popular option. Alternatively, you can utilize programs like PixelHealer, though it's only available for Windows. The rapid color cycling of these tools is designed to help cycle the pixel's transistor and unstick it. If you or someone in the room with you has photosensitive epilepsy or a similar condition, please be cautious when using pixel-healing software.
Fixing a stuck pixel with pressure
To attempt a fix with pressure, you'll need a pointed (but not sharp!) tool like the cap of a pen, a stylus or your own finger, as well as a soft protective barrier, ideally a microfiber cloth. Cover your tool with the barrier, then with the screen off, locate the area with the dead pixel and apply light pressure. Then, while still applying pressure, turn the device back on and check to see if the pixel has unstuck. If not, you can repeat this cycle a few more times.
Fixing a stuck pixel with heat
For this final method, first turn your device off, then warm a cloth — you don't want it to be hot, just warmed — and place it on the stuck pixel area for a few minutes, then power the device back on. Like the pressure technique, this can be repeated a few times if it doesn't work on the first attempt, but taking longer breaks between sessions is advisable to avoid heating up other internal components too much.