it was at that point that I understood / realized that I wanted to be a doctor . At that point in the past, you had this revelation. It began then, and still is true, unless you say that you changed your mind.
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AnonymousLast year I realised that I wanted to be a doctorThat's fine.
Anonymousit was at that point i realised that i WANT/WANTED to be a doctor'wanted'. In the context of a past realization, which took place in an instant, 'want' takes on the flavor of 'start to want', which it doesn't have in "I want to be a doctor". So whether you still want to be a doctor or not, you only 'started to want' ('wanted', in that sense) to be