I'd say it's possible, give that the anemia and possibly the other blood disorder are really life-limiting (as is the migraine situation), from what you're saying. Right now, though, it's not really worth trying, since you're a minor who's not out in the working world.
Since you have a social worker, this is something you should discuss with her. She's much more accustomed to dealing with this kind of thing than most people here would be. When the time comes, you should also consult an attorney who is experienced with helping people get disability.
That your mother didn't get it is irrelevant. These things are decided on a case-by-case basis, and presumably, your medical issues are not the same as hers.