You are a decent person - and a *potential* Righteous Gentile.
You have realised that the Messianic movement was founded by Christians, and that it has no link to Judaism. And you are, AS a decent person, uneasy with claiming to be a 'messianic jew' when you know, you are NOT a Jew, and you don't agree WITH Judaism.
You have a few options here:
1 - just call yourself a Messianic. Or a Messianic believer in Jesus.
2 - embrace your worship of Jesus, and call yourself a Christian: you worship Jesus AS Christ, after all. You don't NEED to 'convert', you ALREADY believe and worship as a CHRISTIAN.
3 - be a Christian but STILL enjoy GENUINE JEWISH customs and rituals, by joining us in a GENUINE JEWISH SYNAGOGUE.
If it would help, refer your mother to info about the Messianic movement. I'm sure she would hate to MISrepresent Judaism, as she is doing now without realising. Maybe you can BOTH worship together in Church - and also come and join us in a genuine Synagogue!
But PLEASE, do STOP claiming to be a 'messianic jew'.
Be honest - as G-d commands US ALL.