You're definitely right in underlining the multistage nature of the process, and that a proper, mostly sovereign identity must be constructed before the ground can be prepared for the next phase. I just don't see how the social construct of racial identities even start to help with that. Not that they even remotedly apply to reality, unless if you start to intersect down so many layers that the racial group identity still matters anyway. Of course I'd wish to fortify that girl's sense of identity - but I'd seek to ground it in individual, incarnated experience, both more intimate and real that group identities or self-concept. A sport like rock-climbing, taking the gramps on an outing, a walk in the forest, real grounding experiences don't need conceptual analysis to bring fruits.
Obviously I'm not saying the girl who's cutting herself needs to learn to appreciate her ancestry. That's not the analogy I was making. The point was rather that the medicine needs to match the injury.
Historically, a certain degree of pride in and love for one's group is a necessary element of a healthy identity. That doesn't just mean race (according to the contemporary definition); it includes all levels: family, nation, species, etc. If there's an interruption at any one of those levels, I think it has a deleterious effect on other levels as well. Thus, someone who has learned to really hate their parents often has a difficult time building a healthy emotional foundation: since you came from your parents, if you hate them it's hard not to hate yourself a little bit, too.
Regarding race being a social construct, this isn't really true; or rather, it's something of a language game. Historically, race meant something much closer to clan or even family. Later it came to apply to wider ethnic groups, e.g. the Germans are a race, the Celts are a race, etc. Later still it came to apply to continental origin, hence Asian, black, white, etc.
The 'social construct' argument partly relies on this historical mutability of the word's definition. However, each of these is an actual, existing social group, with cultural and biological ties. That the definition changed to encompass wider groups of looser (i.e. historically more ancient) ties doesn't change that; and really it just reflects the widening perspective of the species, from the immediate valley of your clan to the entire world. Germans and Celts got folded into White because, once there's a global perspective, it's quite obvious that they have more in common biologically and culturally than either to with the Bantu or the !Kung (who get folded into black). It's really just a question of granularity.
'Social construct' as a term is often used to strip validity from something, as it implies that it isn't real and is therefore of no value. However, we are social animals; it is precisely in the social sphere that we find meaning. This Forum is itself a social construct; that clearly doesn't imply that it lacks value, or that it isn't real, or that it's meaningless.