I agree with you that she is acting irrationally, and am also confident you
have no intention of causing offence. However, please be aware that there is
a difference between "strong emotions" (from which Leah is undoubtedly
suffering right now) and "mental illness".
Mental illness is a malfunctioning of the brain, whereby it behaves in such a
way as to cause detriment to the human suffering from the illness. The term
is also often used to refer to what I would call "alternative mental wiring",
where the 'malfunction' is both permanent and harmless. Leah does exhibit
such an alternative mental wiring (being transgender), but (as you have
mentioned) that was not to what you were referring. In case it needs to be
mentioned, I in no way condemn or believe such alternative mental wirings to
be problematic; I myself exhibit one, and am not at all ashamed of it.
High emotions often cause similar symptoms to certain mental illnesses, but
they are not malfunctions. Rather, they are a core part of the human body's
defence mechanism. Irrationality is not a failing of these, but rather a key
part of maximising mental agility in situations where it is needed.
Whilst I honestly do believe you had no intention of harming anybody, please
do be aware that calling sudden outbursts of irrational or childish behaviour
"mental illness" helps reinforce public stigma against and misunderstanding
of mental illness. Recent public discussion of such issues has been extremely
problematic in this regard, no doubt due to the presence of a high-profile
political candidate whose behaviour is extremely offensive to an array of
different groups, and it is thus particularly important now to ensure "mental
illness" does not become synonymous with "offensive/irrational behaviour".
Once again, please note that I do not take offence at your choice of words. I
just hope you realise the potential damage such applications of the term
"mental illness" cause, and will consider attempting not to use it in such
contexts in future.