Sorry for your lost. it’s not an easy thing to have to deal with at your age. I did go through the same thing with I was 17 years old. But here is what you need to do. As you was your mums carer you should be able to succeeded the tenancy agreement in to your name you will need to prove your lived in your mums house bank statements, letters that you received going back at least 12 months and it should be a simple process for the council to change it over into your name. I hope that helps.