If by "with the star thing" you mean a star shape on the antenna, then you have a Tamagotchi Connection v4.5.
The TamaTown site for that model can be accessed through https://www.bandai.com/tamagotchi/ Slowly scroll down the page until you see a little tab in the middle that says Open. Click it. Links to TamaTown for v3, v4, v4.5, v5, and MusicStar will appear.