My Daughter Bleached Her Teeth for the First Time and 45 Mins After She Had White Spots on Teeth?

White spots that appear on teeth after bleaching can occur when there are hypocalcifications (under mineralized tooth enamel) on teeth prior to bleaching. This is more common on younger teeth that may have been exposed to too much fluoride. They tend to fade somewhat and will not apppear as noticeable within a week or so. Whitening should not be performed on patients under the age of 16 as the pulpal tissue (nerve, blood vessels in the center of the tooth) can be very large in teeth that are still developing internally. .

You did not state what type of whitening your daughter was using but a common side effect of whitening in the beginning is to develop white spots before the color blends in.  Not to worry about it and have your daughter continue using the whitening product. 

Tooth whitening products will whiten enamel including existing white spots which are not normally very visible until after bleaching.  These will fade after a while as the effects of the whitening fade.  These spots can be removed with a technique called micro air-abrasion and may need to be bonded as well.  Your dentist should be able to advise you on the procedure.