"...and feeling that I must get a diagnosis now or never"
The process of giving the girl a throat examination has become rather a battle of wills and to a certain extent a physical battle as well. The Doctor is beginning to feel rather a fool because something as basic as looking down her throat is becoming a monumentally difficult task. He is aware that the battle has gone on rather a long time now and also aware that the child's parents are beginning to lose faith in him. Perhaps he is even losing faith in himself. He realizes that he must redouble his efforts and get a diagnosis of her condition, or else give up completely and leave. This is the precursor to the rather violent show of force that follows.
"I had fallen in love with the savage brat".
This is a disturbing and shocking admission by the doctor, who is also imparting the information in a very scientific and matter-of-fact way as if it is part of a run of the mill home visit. It is more troubling because although he admits that his feelings and behavior are irrational, he does not classify them as inappropriate or completely deviant even though he has stated throughout the story that this is a young child he is visiting with. He calls her a savage because her behavior towards him is more feral and wild than it is childish and frightened. He also finds himself captivated by the expression in her eyes. It is as if he holds her responsible in some way for the irrational way in which he is behaving.
"(the child) claws instinctively for my eyes"
The doctor is specific in his descriptions, and scientific in his observation, which is why it is very impactful when he uses the word "clawing" to describe what the little child is doing to defend herself. Clawing is something that might be done by a cat or a bird, a wild creature not a human. Even if she was attempting to hurt him with her fingernails it would be more usual to say that she was scratching at him wildly. His use of the word clawing is another indication that he is seeing in her something wild, rather than something childlike. She is terrified of him and is acting in the most basic and animalistic way in order to defend herself.