There's both regular and extra-strength bug juice as my derm calls it. Switch derms for sure -- that's a ridiculous amount of money to pay for something that's not working.
What really worked wonders for me to get rid of a plantar wart on the sole of my foot that I'd had for literally decades was a compounded ointment of salicylic acid and 5-fluorouracil. It's heavy-duty stuff and you have to be super-careful about taping off areas around the wart because it will take healthy flesh right off, but it killed the wart I'd had since I was 8 (and I'm now 55).
I'd still start with bug juice for my kid, but know that this is an option (and you need a new derm who will pursue new options).
I didn't get this brand name but I think this is basically the same medication formula my doctor prescribed, although mine was in a cream not a glue base:
https://www.wartpeel.com/media/cms/wart_3F89A0F1CB203.pdf