@mhoye Sounds like an introvert to me.
Introverts are not (all) shy. Some of us can be quite outgoing, but it takes some emotional and intellectual energy, so we need a little "caterpillar time" alone to rest and recover our social energy.
PS: Your daughter is a genius.
@Karen5Lund
there are even different definitions of "introvert" and "extrovert".
The common one:
introvert = shy
extrovert = outgoing
The other one:
introvert = loses energy when socialising
extrovert = gains energy when socialising
And I find the latter much better.
@mhoye