My daughter had her adenoids and tonsils removed when she was a young three year old (it was in November, she'd turned 3 in September). We are very, very glad she had the surgery. She had periodic fever syndrome - every five weeks or so, she'd get fevers running from 104-106 degrees, lasting for 4-5 days, with no readily diagnosable underlying illness (no strep, no ear infection, no anything). She was taking alternating does of Tylenol and ibuprofen every few hours to keep her from being horribly uncomfortable. Our bigger concern, beyond dosing her heavily with anti-fever medication for one out of every five weeks, was that we were getting accustomed to her high fevers and getting a bit lax about dragging her to the doctor to be poked, prodded, tested, and dismissed with "it's probably just a virus". We were worried that we could no longer rely on a high fever as a signal to us that there was a real illness - like what if next time it really WAS meningitis, but we figured it was just another round of fevers? Our incredibly amazing pediatrician finally figured out this pattern, identified the fever syndrome, and pediatric specialist recommended tonsillectomy/adenoidectomy as most likely curative treatment. Since her tonsillectomy/adenoidectomy, her crazy fevers are gone. It's been AMAZING. Definitely 100% worth it for her and for our entire family.
Now, for the actual surgery and recovery: anesthesia is scariest for parents, because parents tend to freak out when they see their child looking unnaturally still. Our daughter had no major problems with the anesthesia: went under just fine, came out just fine, no concerns. The rough spot during her immediate recovery was nausea. She ate a bit the same day after surgery, but pretty quickly threw it back up, which made her scared and sad and was painful. She ended up staying overnight in the hospital so they could keep her hydrated and make sure her pain was under control. It was sad for me, but she has literally no memory of it. She has seen pictures of herself at the hospital, but doesn't associate those pictures with a negative experience. Once we were home, she slept, a lot. We made sure to stay ahead on pain control - don't wait for the child to show evidence of pain, just stay on a dosing schedule and keep it under control before it flares up. Our daughter was really weepy for the first few days when not asleep or watching videos, then she was clingy for a few more days, and by the next week the only lingering issue was we had to be mindful not to serve crusty bread, crackers, tortilla chips, or other "sharp" foods. It really, genuinely went well. She bounced back really, really fast.
My number one tip: bring more than one full change of clothes for yourself (including undergarments! my bra had vomit on it, so I walked around with arms crossed over my braless chest whenever I had to speak to medical staff, looking all gruff, when in fact I was just hiding breasts). Bring yourself some snacks and drinks in case you're there for the long haul. Audio books, whatever. You may be spending a lot of hours in the hospital, and it gets LONG when your child is sleeping or staring mindlessly at awful cartoons.
Wishing your child a rapid recovery!