Hello! I know this is late, but hopefully it will still be useful :)

It's called an escudo de monja ("nun's shield"), and it was a devotional item for nuns in Spain and its territories in the seventeenth and, increasingly, the eighteenth centuries. It began as a tradition of the Mexican Conceptionist orders in the 1630s. Since the 1400s, nuns in these orders had been required to wear veneras (religious jewelery with an image of the Virgin Mary). In 1635, the Archbishop of Mexico made some small reforms to the dress regulations of these convents which included

(nuns must) wear on their cape and scapular an image of Our Lady, surrounded by the rays of the sun and wearing a crown of stars on the head, in a setting that is plain and decorous, which is not to be of gold, stone, or enamel.

(previously, there had been no restrictions on material, and many of the orders were using precious stones or metals).

So in response, Mexican Conceptionist nuns began wearing small paintings either done on copper, or on parchment framed in tortoiseshell, both of which were quite luxury items but still followed the rules set out by the bishop. It also signified a kind of togetherness for the Conceptionist order (other orders forbade the wearing of jewellery or ornament), and became a symbol of belonging for them.

Some other examples of nuns being depicted with their escudos: here, here, here.

Elizabeth Perry has researched extensively on Sor Juana, escudos, and miniature paintings in New Spain - this article is a really interesting investigation into the possibility of Sor Juana as the painter of a number of such items (including her own), and if you have ProQuest access, her PhD thesis is available as well.