Yes, this area of your face can be pierced. Most people call them Dahlia piercings.
So long as the initial jewelry can accommodate for the initial swelling, it’s a pretty straight forward piercing so long as the piercer is experienced, the placement is correct, and the jewelry is of an appropriate material/finish.
As with any oral piercing, there are risks to your oral health you should be aware of. You can read more about that here.