Yes, oregano is safe for children. If she has been this sick all year, I have to assume she is on a diet of meat, dairy and processed foods. I would also assume she has probably had some immunizations in the last year. They say you should never assume because it makes an ass of u and me, so if I am wrong, don't hesitate to say so. If I am right, then the juice diet she is on now is probably the best thing you can do for her - especially if you are juicing the fruit yourself.
If she were my daughter, I would go to a health food store and find a liquid combination of echinacea, yarrow, peppermint and elder flower. This combination is know under several different brands. If it is made by Christopher's, it is known as Kid-e-well. If it is made by Herbs For Kids, it is known as Yarrow Blend. If I couldn't find this, I would pick up some type of echinacea in a glycerine base. Then I would give her 2 - 4 dropper fulls every hour when she's awake to boost her immune system.
If you can find some usnea tincture - this can be put in some water and works really well on strep throat. You can also use the oregano in the same way - the oregano could also be mixed with some olive oil and rubbed on the throat. To bring the swelling down in the tonsils, I would use either some mullein and lobelia ointment (look under Christopher brand) rubbed onto the throat with a little cayenne ointment or I would make a strong tea of 3 parts mullein to 1 part lobelia, soak a cloth in it and wrap it around the throat.
I hope this helps, Dr Mom