Are Just Around the Corner?

A time or event that is just around the corner is coming very soon: It's still cold today, but spring is just around the corner.

Which is correct round the corner or around the corner?

If you say that something is around the corner, you mean that it is very near. In British English, you can also say that something is round the corner. My new place is just around the corner.

Which is right around the corner?

"Right around the corner" - in this case the meaning refers to the near future; it means it is about to happen soon.