Since you got it just yesterday, you're probably on generation 1. Your Tamagotchi character therefore was an orphan - having neither parents nor grandparents. That's why you can't get into the family menu.
Once your current Tamagotchi character gets old enough (when its about 7-10 days old) it can have a baby. After the baby is old enough, the adult will return to Tamagotchi Planet, leaving the baby in your care. This baby will be generation 2. Once you are at this point, you should be able to view parent information in the family menu.
If you take good care of the baby, and it lives to be an adult, it can mate and have a baby of its own. Once the generation 2 adult leaves, this baby will be generation 3. With it, you will be able to view parent and grandparent information in the family menu.
