Well its still possible that someone found Toumas ripped off hand from that sport festival and the dragon was somehow attached to it. Maybe they did experiments in that prison and this girl got blood from Toumas found arm. Blood allowed to summon that one dragon
The girl saw that dragon and her esper power allows her to copy stuff she sees which might act like Aleisters blasting rod... so it uses imagination to attack...like the thing gets as strong as the opponent sees it. Mikoto saw that dragon when Toumas stopped her and knows how strong it is... so the dragon recived similar image of power.
She is Toumas half-sister XD Touya was a playboy on one point in his life too
so she got a weaker version of the right arm. If not IB Touma could summon those without losing his arm.
But I wish Touma would be involved in this...girl sees that guy on her path attacks him with the dragon...but dragon stops in front of him...he pets him like John Snow from GoT and dragon returns back home into Toumas arm xD (or she uses 1 dragon and from Touma came out 7other dragons....girl pees herself...her dragon lives her arm and returns to Touma leaving her in shock)