She needs to see a psychiatrist.
It is not the case that a psychiatrist will take weeks to prescribe meds.
He/she might do this after the first visit, and, if needed is bound to do so.
I would stop trying to control the choice, and urge your sister to go forward with the referral.
We do not give personal recommendations for referrals on this site, but in case her new doctor does not work out, here is a list of psychiatrists in the area who are board certified.
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