Grief?

A young child whom I was particularly close to lost her mother last year. I was very affected by this. I had some similar feelings to grief although I had only met her mother a few times. I started to be depressed, my anxiety increased, and I disassociated some. I also developed a few strange coping or maybe destructive methods of dealing with it all. I wrote letters to her mom updating her on how her child was. I started saving cards and writing down details from/about different people. I wrote an unofficial will just in case I died. I almost started feeling all the emotions I will eventually feel when those I love pass away. I’m wondering what is this and is there an official name for what I experienced?