My daughter had hers out in April. Had a horrendous time post-op. She developed an infection (keep your nose alert for horrid breath, like rotting skin. I thought that the smell was a normal part of the wounds healing, but it was actually a bad infection). She got medicine for that. Four days after her op, she spat out some blood when i was brishing her teeth. I called the ENt ward and they advised to bring her in. They couldn't see any bleeding on the tonsil beds at all, and there was no further bleeding, but kept her in overnight as a precaution.
Then three days later, a week after the op and seemingly feeling much better, blood gushed out of dd's mouth after dinner. Totally out of the blue. She'd been full of energy and smiles all day before that. I called ENT. They advised me to hang up and call 999 instead, which i did. I put her over the bath until the paramedics came. And loads of blood just kept coming out all the way to the hospital. We had to wait on her surgeon getting called in from his home. He said that she had hemorrhaged, which is very rare. She went for another op that night. Afterwards, the surgeon told us that another vessel looked ready to burst during surgery. rather than leave it, and therefore needing another operation to heal it when it finally burst withing the next day or so, they just burst it fully while she was already in surgery.
Anyway, after that, all was fine.
Complications following tonsillectomies in children are rare. But they do happen. If you have any concerns at all, i can't stress enough to see the GP as quickly as you can, or to call the ENT ward for advice where your daughter had her op.
So sorry if this all sounds a bit scaremongering. But i hope it's helpful? The whole thing really shook me up.