Horner's Syndrome?

When my daughter was 6 months old, we noticed that one pupil was larger than the other.  Her pediatrician examined her and told us it was nothing to worry about.  A few months ago (my daughter is now 7 yrs old), we noticed that she has a slight ptosis in one eye and that one eye blinks more than the other.  We recently took her to an ophthamologist, who diagnosed Horner's syndrome, "probably due to birth trauma".    She does not appear to have anhidrosis or heterochromia, and she had a fairly easy birth (she was only 6 lbs), so I'm a little unsure about this diagnosis.  Is there anything else I should be looking into?  On a side note, she also has had severe asthma since she was about 9 months old, has food allergies (eggs/peanuts), and has always scored 1-3 percentile in growth.