Actually, once your Tamagotchi is an adult you can play games to get Gotchi points. It's not a lot of points but enough for the Tama to get by. Sort of.
So, the way you do it is go to the 5th icon (door) and scroll to "away." Then your Tamagotchi will take off and you press button B so you can see them. Then it will show a strange surfboard music shop. You can't get money from that, so press button A. You will see a bakery. You can get money from playing this minigame, so you can select that. Or press button A again and you will see a fruit shop. You can get money from this as well. With these minigames, the Tama's stress can go up and you will get less than 500 Gotchi points (as far as I am aware).
However, it's easiest if you practice with your band, even just a little, because you can get tons of points from hitting the top of the music charts. Like, MILLIONS of Gotchi points. It's not too hard to practice with the band every so often and have a MUCH healthier and happier Tamagotchi.
I'd recommend reading the Tama's instructions when it arrives, so you understand how to play the games, et cetera. Or find the instructions here.
If you're having trouble with the Tamagotchi, don't hesitate to ask away!