Follow your advice. Your allergist has likely confirmed the diagnosis by now; if not, your baby should be evaluated - the specific foods causing reactions may not be the same as those that bothered you. Once you have a confirmed list of all the foods to which your baby is allergic, you need to carefully eliminate all of them from your baby's diet, in order to increase the chances that they will be outgrown.
It depends. It depends on what kind of allergy your child has. You should have your child evaluated by a doctor and possibly see an allergist if she has not already done so. Once your child is diagnosed they will give you a treatment plan. You should then be educated how to prevent and treat her food allergies. You should also be sure everyone else who cares for her is educated in the same manner.