Konjunktiv with present meaning:
An important thing to know about the German Konjunktiv is, that although the Konjunktiv II is derived from the Präteritum (which is a past tense), its meaning is present.
So you have:
sie ist (Präsens Indikativ) - sie sei (Konjunktiv I) - sie wäre (Konjunktiv II)
All these forms actually have present meaning - even sie wäre which is derived from sie war. That's not too different from English which also has two subjunctive forms:
she is (present indicative) - she be (present subjunctive) - she were (past subjunctive)
These forms refer to the present, too. (I suggest that it be removed now.; If she were ill today, she would...) Even she were has present meaning, although was/were normally is the past tense.
Of course there are differences in usage of English subjunctive and German Konjunktiv.
Konjunktiv with past meaning:
Now, if you want to form sentences with a past meaning you need to use a perfect tense and take the Konjunktiv/subjunctive of the auxiliary verb. The German auxiliary can be sein and haben:
sie ist gewesen (Perfekt Indikativ) - sie sei gewesen (Perfekt Konjunktiv I) - sie wäre gewesen (Perfekt Konjunktiv II)
sie hat gebraucht (Perfekt Indikativ) - sie habe gebraucht (Perfekt Konjunktiv I) - sie hätte gebraucht (Perfekt Konjunktiv II)
Analogically, in English you have (only have as auxiliary):
she has been (indicative perfect) - she have been (perfect subjunctive 1) - she had been (perfect subjunctive 2)
Application to your sentences:
Now your sentences were
Sie war gesund. Sie brauchte die Ärztin nicht.
Both have a past meaning and you want to put them in the Konjunktiv II form. So you need the forms sie wäre gewesen and sie hätte gebraucht:
Wenn sie gesund gewesen wäre, hätte sie die Ärztin nicht gebraucht.