Oh yes they can. I would call the vet and tell them what type of worms you are dealing with. They can give you the proper wormier or better yet I would take a fecal sample in and let the vet decide what to treat.
You have to worm both dogs if you have both dogs. Wash all bedding, clean up all the poop outside so they don't smell it and re infest them.
In about 10 days you need to worm them again.
What I do with Wiley and Blaze, I have two different wormers. I use safeguard one month and then Ivomac (sp) the next month. With the type of stuff my dogs get into I have to worm this often.
You may not have to do it this often but over the counter wormers are junk.
Did you get the shot records and worming records from the vet when you got the puppy?
I'm also concerned that you have such a young puppy. How long have you had the dog? What breed is it?
The puppy should have been wormed at least twice by now, usually every 2 weeks, since puppies are either born with worms, or they can be passed along to the pups from the mother, even through the milk.
Your puppy seems very young to be away from the mother and the other puppies.
If your puppy hasn't went to the vet yet, just take the puppy in. It should have been wormed a couple times already, but I don't start vaccinations until 8 weeks. If you want to wait until the vet can do the first shot, you can always take just a stool sample in and have it tested. Then they can see which is the most appropriete wormer to give-- I would be guessing something with pyrantal pamoate as the active ingredient, but maybe that is only the primary puppy worms in my area (round worms). The vet can also check the sample for other things that may need to be treated, like coccidia.
Good luck with your new puppy-- and DON"T try any wierd home remedies on a puppy. Over the counter wormer at the grocery store isn't even very expensive (worst case scenerio, just use that).
It's normal for puppies to have worms, but that's why we worm them at 2,4,6,and 8 weeks of age; so that when a family gets the puppy, it has no more worms. Yes children can get them, and so can adults and other pets. How old is your puppy, and what breed is he?
Dogs having worms in general is normal. Preventative worming is important at all ages - especially if you and your dog frequent places that other dogs go. Dogs getting worms is like people getting colds or the flu... they just kind of share.
Puppies are often born with worms - but even if they aren't, because their immune systems are still developing they have almost no resistance to parasites (their mother has a low resistance to them when she's pregnant as well - which is why they often get passed to the puppies). Therefore, during the entire first 6-12 month of your puppy's life you really should periodically worm them. Some puppies don't show loose stools until they have had a parasite for weeks.
They are nothing to get stressed out about - but something to be aware of.
I prefer Panacur/Safeguard as a general wormer. I don't mess around with the other basic kinds like Strongid or Nemex or anything Pyrantal past 4 weeks of age. Panacur hits multiple parasites (including Giardia if given an extended dose).
With a 6 week old puppy, talk with your vet about a worming schedule. I'd recommend a 5 day dose of Panacur right now, and then 2 weeks from the last dose, do it again. Then every 6-8 weeks until your puppy is at least 6 months old I would repeat at least a 3 day dose. Parasites can cause stunted growth and developemental problems if left untreated - and like I said, they don't always have loose stools right away.
If, afer the Panacur the stools don't clear up, you'll want to run a stool sample and see if you're dealing with Coccidia or a strong case of Giardia - in which case you'd want to use a different wormer (Albon or Metronidizole/Flagyl).