The appropriateness of using the term "mommy" as a term of endearment or a nickname for your girlfriend depends on the context and the preferences of both individuals involved in the relationship. If your girlfriend is comfortable with being called "mommy" and it is something you both find endearing and enjoyable, then it's okay within the confines of your private relationship.
However, it's important to be aware that some people might find this kind of nickname uncomfortable or strange, as it can have connotations that extend beyond the romantic context. It's essential to be respectful of each other's boundaries and preferences in any relationship.
If you both feel good about using this term of endearment, there's no issue. Just ensure you have open communication and mutual understanding, so both of you are comfortable with the nicknames and pet names you use for each other.