I would go forth without asking her verbally 'what's wrong', but looking for clues and cues. This is a touchy situation; outside a psychologist, I'm not sure I could offer concrete suggestions for the deeper problem of her aversion to medical care. I worked with a child years ago who had had multiple heart surgeries by the time he was three and suffered some hard challenges because of this. It's really tough for the kids and their parents.
If it were me in a situation where I felt I wasn't getting good feedback, I'd go with my gut as to when to seek medical care and when to wait and see if it was a passing bug or something worse. Some symptoms (severe pain, vomiting, redness, swelling, bleeding, fever) cannot be suppressed, even by a non-communicative person, and those are the most severe, so that's what we have to go on, much like when she was a baby.
I'm sorry this is such a tough situation-- good luck to you. You might consider a private conversation with your daughter's pediatrician over the phone, so that he/she would be able to talk with your daughter about her communication during the next visit-- or the doctor might know of someone to refer you to if it's agreed that this needs to be addressed more directly by a counselor.
Lastly, there are some kids who can have pretty good energy while they are sick. I grew up being kept in bed all day when I was sick, and was surprised to learn as a nanny that some kids 'do' sick differently. I say, as long as she's happy and comfortable when she's ill, and getting some rest times (read stories-- this mellows kids out), this will likely be better for her than being miserable in bed. Good luck!