Who I have the same questioned this topic

I just got an S9 yesterday, I had an S7 before. When using Messages+, I have multiple conversations that are now showing up as Group messages, but it is only between me and one other person. The weirdest part is, it says that "Me" (which is obviously my phone number showing up) is one of the other group members. Then when I send a text, it delivers it, and then I also get what I just sent, back as a reply... Very Strange. Any ideas?