In this sentence, braces most likely refers to dental braces, which are used to straighten teeth. It would make sense to feel self-conscious about smiling due to having these visible on one's teeth, especially when first getting them.
A "tank-top" might be referred to as a vest or sleeveless shirt in other English varieties, but this wouldn’t typically make someone self-conscious about smiling. Similarly, braces would not refer to dental crowns, which are caps placed on teeth, as these are typically less visible and wouldn’t cause self-consciousness about smiling.