conversations on my ipod are showing up on my iphone

I have 2 ipod touches and an iphone on my apple account. One of the ipods belongs to my grandson. Today I got caught in a 3 way text converation between my grandson and his friend. As the title states, it started showing up on my iphone.

I currrently have the person from today set with no audible notification for text messages. What I would like to do is keep it from showing up at all. Is there any way, short of setting up a seperate account, to keep conversations limited to the device being used? If not, I can do that, just prefer not to.

Thanks in advance for any assistance you can give me.