Είναι επείγον! Θέλουμε να δούμε τη γιατρό. / Πρέπει να δούμε τη γιατρό. / Χρειαζόμαστε γιατρό!
/ Πρέπει να δει [τη] γιατρό! (the patient being the subject) / Πρέπει να τον/τη δει [η] γιατρός! (the patient being the object)
I believe that the prevalent wording among current patients and those accompanying them to the hospital or what-not, would be something along these lines.
Έκτακτο is also OK, but at least to my ears, it sounds a tad stiffer than επείγον: As if the speaker is making some kind of half-conscious, half-arbitrary attempt to speak doctors' parlance.
Γιατρός is by far the most common way of referring to a doctor, regardless of gender.
Both ιατρός and γιατρέσα are obsolete, though the registers they belong to are almost polar opposites of each other, γιατρέσα being a kind of "folksy" term probably still occurring sporadically amongst old people (those with great-grandchildren), whereas ιατρός is somewhat of a warning sign that the person speaking might be thinking a bit too highly of the Greek language's heritage, so to speak...
Cheers!