I would change the order, though 1 and 3 are fine. 2 is confusing.
1. Jane and Peter are next to me.
2. Jane is next to me, on my right. (Jane is on my right.)
3. Peter is on my left.
If I were to put these sentences together, I would use your order for at least one of them. It's just an aesthetic choice.
Jane and Peter are next to me. Jane is on my right and on my left is Peter.