I wouldnt use flea/tick shampoo on a puppy younger than 12 months old.....you can get any brand, but just don't use too much or get it in their eyes....if you use dawn dish soap and dilute it, that helps kill off fleas---i would call your vet if your that concerned!
I do not trust HARTZ products as in flea/tick topical things or collars, ive seen them kill dogs and cats, but i will use their shampoo....
Good luck.....