Our DYS/SET 13 year old daughter can be socially awkward too (pubescent girl power games are needless and utterly vapid to her) with age peer girls but has often done well with older people and boys.
What helped her was finding a clique of geeky/nerdy yet not altogether unrowdy boys to hang out with. Also, attending CTY residential camps helped her to meet kindred souls - a true balm for her soul - from other cities and states. One of whom has become a very close friend.
From that friend's parents we have learned that fencing is likely to appeal to her and she will try to join the club when she starts high school this Autumn.
Wife and I read Untangled which helped as well - it is apparently very difficult, even for professionals, to correctly diagnose depression in teenagers, especially girls.
While I wouldn't leap into assuming depression, I would keep a weather eye open in this regard.
