I had two young tonsils-out kiddies (DD3 was coming up 4 and DS1 was just 4).
DD3 had to have hers out as every single time she had tonsilitis she had seizures and we had to ring 999....she literally would go from ok in the morning to lethargic by lunch and seizing by mid afternoon and blue-lights to hospital.
By rights she should have had hers out at 2.6, but I was pregnant and so said no, so she waited. She also had to stay in, one night before and two nights after, but she has immune-deficiances which complicated things. It was fine, and the nurses were fantastic. I think for me the scariest but was them having to gas her under as she completely freaked out at the needles. I cuddled her close singing to her whil we waited for the gas to take effect, and then had the nurses pulling me onto a bed.....I apparently breathed in the gas too!!
With DS1 he was having sleep issues (apneoa and snoring etc)as his tonsils were so large they touched the entire time. He was kept in for one night after as he wasn;t great (bleeding), but again, the nurses were wonderful and the doctors kept me informed the entire time, making me feel very comforted and confident in them.
I think anything to do with your child and hospitals is going to be scary, despite any reassurances, it is your child and the love you feel means you are scared. Please believe tho that they have your childs best interests at the top of their agenda and will do their utmost to keep her safe and you happy with her care. Tonsil ops are very common, as are adenoids, and yes it is a bit sore for your child, but TBH, no worse than them suffering tonsilitis anyway.
take care of you tho........you need to be there for your child so be kind to yourself.....I make the mistake of going into a spiral of melt-down........NOT good!