Don't usually means don't, don't want to
Nian means miss, miss
The general meaning is don't think about it, don't forget it.
But I can’t guess the meaning after looking at this
Your girlfriend probably just thought of a good signature, and she feels quite literary.
If you insist that this is some kind of inner expectation or a true thought that is meaninglessly exposed
It can be understood as two meanings
Don’t go Miss someone and don’t forget someone
or
Someone don’t miss me but someone don’t forget me either.
It is still not recommended that you think too badly, just ignore these words.
The first is to be tolerant, and the second is not to destroy your relationship.