OP, we can only say what we *think* we would do in your shoes, based on what you are telling us here, but ultimately you are the mom. But I still don't think you are on that much of a time crunch. Waiting two weeks and doing a total elimination diet to see if three is any change at all is not going to set you back that much.
http://www.askdrsears.com/html/4/T041200.asp
This doesn't cost any money and to me it would be worth a try. That being said, it could be any food, so you could also just try keeping a food journal and eliminating one or two things at a time, but that takes longer. Or you could do a food allergy test, the one my ND offers only costs about $100 and it is just a finger prick.
I personally would also seek out a constitutional homeopath and try that first too.
My concern would be, what is the imbalance and root cause here? If for example it is allergies, and instead of identifying the allergens, you just remove the tonsils, then what else will the body do to compensate for this? This is what happened to me. I got strep throat one year NINE times in a row. And was given antibiotics every single time, which completely set me up for other issues later. After that many bouts of strep, they removed my tonsils. And guess what? I STILL got strep throat! And I was still constantly sick. So finally, after the fact, they turned to other alternatives and tested me for allergies. I was very allergic to cats, mold, and dairy. Even on traditional allergy tests, so I can only imagine what else I would have showed up being allergic to with the alternative allergy tests available today! So, cats, mold, dairy. Well, my room was in the basement (mold), we had a family cat who stayed in the basement most of the time, and I ate a lot of dairy (milk, cheese, ice cream, everything). After eliminating those allergens, I wasn't sick anymore. And I have never had strep again, ever, despite being exposed and taking very close care of people with strep.
I, personally, would want to know that I had exhausted all other options and avenues before surgery, instead of the other way around, as was done to me.