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 rig