Good Morning D.,
I second MommyCakes, try taking her off foods that are commonly known to trigger allergies. First try milk and keep her off the milk for at least a week and see what happens. If nothing, then I would suggest you try taking her off all wheat products.
The reason I suggest this course, when I was a little girl I was always sick with strep throat and tonsillitis. Every winter I got sick and didn't get better until spring. I was on a constant round of antibiotics for at least 4 winters in a row. Finally my tonsils were removed when I was 9 years old and miraculously I was all better.
What the doctors didn't know was I have multiple food intolerances that were making me sick and my tonsils were just the most obvious symptom. I developed multiple indoor/outdoor allergies because my body couldn't figure out what was bad for me and what wasn't. Eventually I developed asthma that is triggered by my indoor/outdoor allergies.
I have since taken myself off wheat, corn, and most milk products and I feel a lot better. When I do get sick, I'm not sick for long and it doesn't trigger my asthma like it used to.
I'm not saying your daughter will go down this path. Each person is very different. But, your daughter's tonsils and adenoids are reacting to something. It is in her best interest to find out what is making them swell. Take away that trigger and she'll get better all on her own without surgery.
If you are interested in discovering your daughter's food allergies and intolerances, I suggest calling your health insurance and ask for references to pediatric allergists. Then call those offices and ask them if they test for food intolerances (many offices don't test for these only for food allergies) and how the testing is done.
I hope your daughter starts to feel better soon.
C. J.