i'm a vet tech, but not near the bronx so sorry can't help with that... but i can tell you that for the kitten they are probably not an emergency - but the reason they should be treated asap is that it can be hazardous to your family members, especially young children. And especially if its round or hook worms.
But you don't want to wait too long for the sake of the kitten too, because kittens with worms don't thrive quite as well and if they're very young it can potentially get very dangerous... it also depends on what kind of worms too but if you're seeing them that means there are a good number in there already.
DEFINITELY don't get the over the counter petstore or grocery store products... for 2 reasons - first, from my personal experience at my job, they generally don't work!! So its a huge waste of money and is a false security that they're gone when they're not. But secondly, some of those treatments use some questionable methods of treatment that aren't always safe and use more chemicals than they need to!! (especially on kittens!)
So my advise - i don't think you need to find an emergency clinic immediately, but definitely in the next few days find a good vet to take your kittens to! And get BOTH kittens dewormed - if they're sharing a litter pan they may be sharing the worms too!!