non unique pipe blockage

I am in a second floor floor flat.

As the washing machine empties, the waste water fills up the kitchen sink and take a little while to empty.

I have been in the flat for precisely two months.

When I first moved in this did not happen.

The previous owner did not have this problem

Do I really have a blockage ??

Yep, it is blocked all right, probably not completley but quite heavily. You may need to have the waste pipe rodded