I'm so sorry. It is so very hard to adjust to living without the only person who has been in your life since your first moment alive.
I felt as you did when my mother died, also after dementia, over 30 years ago and she was older than your mother, being, 70, but still too young to leave me.
It took a long time and many many tears but I did manage to live without her, something I had never thought I could.
I can still cry - starting at this moment - but it's ok to cry at the loss of someone you loved. Loving doesn't stop when someone dies and memories keep it alive which is a good thing.
However, the pain does ease a little. It doesn't go away but just becomes a part of you. It happens very gradually but one day you will realise that you have felt genuine joy about something. I hope life becomes more bearable for you and your sister very soon. x