Treating your puppy for fleas and ticks is necessary to stop an infestation, but you will also need to treat the areas where he sleeps. Talk to your vet about safe and effective treatment for your puppy, which will depend on his age and size; then spend some time getting rid of the fleas and ticks in his bedding.
If your puppy sleeps on an upholstered bed, the best way to get it clean and free of pests is regular vacuuming. When you have an ongoing pest issue, vacuum the entire house at least weekly, and your pup's bed daily.
If your puppy sleeps on machine-washable bedding, wash it in hot water several times a week while you are battling the pest situation. Once the issue is resolved, weekly laundering should be enough to keep the problem in check. Items that can't be washed might be better off thrown away, as they might harbor flea larvae that will re-infest the pet and the bed.