I am so sorry to hear about you mum, OP, and to all who have replied too. 
May I reply from a slightly different point of view? My mum lost her own mother when she was your age, and then went on to have me just a year or so later. She was a very loving mum, but from a really early age, I remember being aware of her sadness, and that loving me was about more than just me. There wasn't counselling available then (I'm quite old!
) and I know that she tried to be positive and not sad in front of me, but I so wish she could have grieved properly and fully, and then in time, talked about her mum, and made her part of our lives, and part of our present: "Your Grandma would have loved to see you play" "Your Grandma would have been excited to see X." Instead, my Mum hung onto her sadness and to memories and to objects and only spoke of her Mum and her own feelings about the past with a sense of tragedy.
It is tragic, of course, to lose your mum so young. But it's a double tragedy if it then defines everything that you do, and choose, and feel from that point on. If you get chance to do so, please please do consider counselling (Cruse, I know, offer brilliant counselling at any point after a bereavement), so that you have chance to get the support that you need, when you are ready to do so, to move forward, with memories which you will cherish but free from the regrets and could-haves, which can be a burden in themselves.
But only when you are ready. You are allowed t feel sad, to mourn, and to move forward in your own time. A year is still very early in your journey
Sending best wishes to you.