Who has time for sadness?

As you are aware, I am a working mom with two very busy kids. I love my life, most of the time. What I miss, is quiet time. I can't recall the last time I didn't have something to do or somewhere to be or someone who needed something from me. Most of the time, that's ok, I like it that way! I love being needed and important in my children's lives, and being a part of my community is important to me too.

That being said...

On December 20th my friend Melissa died. She was a beloved friend who had a very quick battle with cancer. I mean, we were at work together in October! I took her out for dinner on November 25th! Yes, she was ailing, but all signs were pointing to recovery at that time. 3 weeks later she was in palliative care, then suddenly she's gone from the planet forever.
I walked into the care facility and asked to see her, only to be told she had died an hour before. I couldn't even breathe.

And here I sit, at work, in the office I shared with her every day, and the grief still smacks me in the face at any given moment.

So my question is: Who takes time to be sad?
The day she died I sat in my car on the side of the road and screamed and cried for 10 minutes. Then I got on with one of the more hectic days on our schedule, dragging kids to practices and Christmas parties, standing at outdoor rinks and acting as if the world wasn't completely upside down.
I took the next day off and cried all day, but still continued to 'do stuff'.

Then Christmas and all it's chaos arrived, and we were off to hockey and ringette tournaments all over town and then everyone just went back to doing what they do.

Is that grieving? Is that what the process is? Just ignore the pain and eventually you just keep on going?
I feel like I'm walking on a tightrope. My neck and shoulder muscles twang like guitar strings, and I cry at the drop of a hat.
Am I supposed to feel like this? Isn't there something I should DO??? If so, WHAT???
I am lost, like that sad little boy in "Where the Wild Things Are", when his boat floats away. I have no paddle, no compass, no life preserver.

Intellectually I get that at some point I won't feel this lost or stressed out or strung out. My mind recognizes that this is not the first time I have lost someone I love, nor will it be the last, and what choice is there but to keep trudging on? But my soul hurts. My brain is detached from responsibilities and I am just going through the motions. I have no idea what my next task is at work, and am unable to make myself care.
I think I need time to be sad, I just don't know how. How to find the time or how to be sad. Stillness is an imaginary thing to me, and I think the healing lies in the stillness.