At age two my daughter was hospitalized for six days due to a gastrointestinal virus. Since then she is terrified of all doctors and dentists. During her last visit for a physical (age four), she screamed, spat, hit, bit and everything else to avoid having the doctor do even minor things such as hearing test, eye test, and counting teeth. The doctor even suggested counseling. Do you think this is something that she'll grow out of, or does she really need counseling?
The deep-seeded post-traumatic fears and anxieties she has lived with for two years clearly still affect her deeply. I have witnessed these same responses in children within my own extended family -- one was the result of an operation at age four, the other a child's fear of the water based on falling accidentally into a hotel swimming pool at age two. As the years have passed, both have been able to deal much better with the stimuli (medical settings and swimming pools) that they associate with their traumatic experiences. These traumas can not and should not be taken lightly. Let's not forget that at two she did not have the emotional language and sophistication to give voice to and work through her intense feelings surrounding this hospitalization.
I do believe that your daughter will grow out of the extreme reactions she now exhibits when in a medical setting, but she will do so on a timetable that cannot be rigidly imposed on her. I think she is old enough to benefit from working with a talented child therapist who has worked with kids similarly traumatized. Often therapists work with the child's medical caretakers as part of the therapy. My recommendation would be to see what professional help you could bring her.