Should I buy a playmate for an orphaned wild mouse?

I'm taking care of an orphaned wild mouse a neighbor found in her home the other day. I believe she's about 16 days old since her eyes opened the day she came into our care and it's been about two days since then. I know mice are social creatures so I worry about her being alone. I sometimes let her sleep in my hand (in a tissue of course) so she gets the feeling of closeness with her caretaker, but I worry about her sleeping all day. I've found online that the best time to buy a pet mouse is five to six weeks old. I'm wondering if I should get her a playmate once she's that old? I know females tend to not fight amongst each other, and I'm fairly sure she's female, but I'm a bit worried since she's technically a wild animal.