Verrucas are a bu**er to treat .
They can look bigger after treatment because the acid ( usually salacylic acid) makes the skin more mascerated and soggy.
There are good and bad in all treatments, some suit one person but not another.
Duck tape (the heavy duty waterproof stuff) will occlude and mascerate the area ,so when you remove it, a but of the verruca skin comes off.
Some people try nail varnish, it occludes and stays put, bit difficult to prise off though.
Banana skin has an enzyme which breaks down tissue, but you can only use at night ( or it would be impossible to keep in place)
Marigold therapy has different types. One heals ( so for ulcers) one will break down tissue ( so good for verrucas, callouses, fibrous corns)> If your chiropodist uses it, it's worth a try, but again it can be messy.And check how long it has to be kept on and can you get it wet. Or do you apply it yourself.
You could ask if your GP will freeze with liquid nitrogen. It forms a blister so you would need padding on the heel. And you need to bear in mind not all children will tolerate it.
Silver nitrate is quick quick working, so by the time it goes black that's effectively it.
My DD got a verruca swimming last year (on her heel). She didn't like the Bazuka gel, said it hurt her. I had to pad up her heel with felt (with a hole cut out over verruca)
Eventually it went very black, that's the blood vessels, and came off- healed lovely.
They can get itchy when they are resolving,BTW but I would have the rash checked. Might be something rubbing or might be sign of infection.
I'd love to offer you a quick soloution but there aren't any 
Might be an idea to get a verruca sock, just in case.
And if you do need to keep the dressing dry, there's a product called seal-Tight which is a waterproof sock for bathing. You can get them on prescription. OTC they are about £28.