There is no specific name for that particular sibling which would make it clear to the listener that you have two younger sisters and you're referring to the elder of the two. There are two points of age-comparison: she's younger than you but older than the youngest. 'Middle sister' could be taken to mean that you have three sisters.
It would obviously be ridiculous to call a 6-year old girl a young woman. What's the youngest age when it's no longer weird to call a girl that?
What is generally considered the youngest age at which it's normal to ...
Old: Directed by M. Night Shyamalan. With Gael García Bernal, Vicky Krieps, Rufus Sewell, Alex Wolff. A vacationing family discovers that the secluded beach where they're relaxing for a few hours is somehow causing them to age rapidly, reducing their entire lives into a single day.
my [young / younger / youngest] sisters - English Language & Usage ...
To me, younger is preferable to youngest, not least because it seems an odd choice to define 2/3 of a group with a superlative. The oldest child is the only one who isn't younger than any other child -- thus, younger children is quite clear.
His sister is his youngest sibling, but his younger sister. Since she is the lone female child, there is no need for the superlative form. Suppose, however, that there are more siblings, and their birth order goes like this: boy, girl, boy, boy, girl.
He was one of the youngest of his siblings. The meaning should be clear: he had many brothers and sisters, and he was one of the youngest of the lot, but the expression feels awfully awkward to me, with expression his siblings implicitly excluding the subject from the set; you're not your own sibling, so you're not one of your siblings.