Is it possible to do any piercing on yourself? Technically yes. Putting a needle through your skin and adding some jewellery is not the hardest thing in the world, but doing it properly is not so easy.
Doing a couple of nostril piercings, say, means working with one or more mirrors. It’s all upside down and backwards. You can’t see what you are doing, only a reflection, and that makes it harder, though not impossible, to get good results.
This is one reason you go to a professional piercer. They can measure you up, but also cast a critical eye over the markings, to decide where it should be placed to look right, given the wonkiness of your anatomy.
However, it can be possible to pierce your own anatomy with real results, provided you can see it and have easy access.