Receiving my own text messages in group text

When another person sends me a picture, I receive it in a group text that includes me as a recipient. No problems when they just text me. I have to start a new text thread with that recipient in order to not continuously group text myself after they've sent me a picture. I don't want to turn off group texts, however, as this would cause even more chaos/disorganization of texts. The other person is an Android user. I'm not sure if this makes a difference. Has anyone else experienced this and is there a way to fix it?