I don't think there is a right or wrong way to grieve. As far as writing to strangers, I've been doing just that since my dad was diagnosed in August. I too have had tears daily since that date. Perhaps I'm grieving ahead of time as well.
My dad is still with us, although not for long. I'm not sure how I will react at the end. I think that however you react is fine. My mother-in-law never cried when my father-in-law died because "he didn't suffer," "he had a good life" and according to her "I still talk to him everyday."
It's never a bad idea to seek help though. Especially losing someone as close to you as your mother clearly was to you. Definitely keep talking about her to friends, people on this sight, or professionals.
I'm sorry for your loss.
Cheryl