Can tongue piercing make you depressed?

Probably not, depression useually has much deeper and more substantial causes than a simple piercing. A minor event may trigger an episode of depression, but the cause is usually something else.

For example:

A person drops and breaks a coffe mug, and it triggers a depression event. In counselling she reveals that she was often beaten as a child by her parents, and recalls events when she was beaten for acidentally breaking dishes; which is the cause of her depression.