A 7 week old likely is about due for a vet visit. The vets have the safest and most effective flea remedies. Long term, I would talk it over with your vet and go with what seems best for your particular case. I wouldn't use anything without reading the label to verify it is safe for a 7 week old.
I am not sure what would be the best to give the puppy relief until you make it to the vet the first of the week. Maybe try a flea comb plus some over the counter flea spray for any rugs and other furnishings the puppy is around.
If you check the sticky at
http://www.askmehelpdesk.com/dogs/in...tml#post251802 you will see I don't recommend bedding for puppies. I have never had problems with fleas on a new puppy, but they may be one more reason not to use bedding. Maybe not using bedding is part of the reason we don't have flea problems.