Did she die because I told her it was okay to?

A question that runs though my mind a lot the past few months. I know mom would have died anyway, the cancer was just to much for her or anyone to handle.

2 days before she passed away, mom asked me while in the hospital if I would help her with a shower, she told me she could ask the nurses, but felt better if I helped her instead. I of course never had to think on it, I just did it she never questioned being a mom to us, she just did it.
I gathered everything up we needed. shampoo, body wash, bath poof, and clothes. we headed down the hall, mom in a wheelchair with her oxygen, and I was carrying her things. A nurse helped us get arranged in a shower room.
With mom being in so much pain it was a slow process, we only proceed when she gave the okay to.
The nurse left after mom was sitting on the shower seat. I got the shower running, got her favorite body wash (olay ribbons) and the bath poof. I got on my knees at her feet, and started to wash them.
I felt her hand on my shoulder and as I looked up seen her eyes filled with tears, and she began to cry.
I asked her if we needed to stop, thinking she was just in to much pain to continue on, she just cried, I asked her again what was wrong, she told me she could not fight anymore, "I am tired" she said.
And I told her it was okay to stop fighting, it was okay to die. I knew her pain was too much for her to handle.
The next day it was clear she had made a change and the doctors felt it was time to call in family to say goodbye.
I know she did not die because I told her it was okay to die. but deep down in the pit of my gut, I feel like I was the one who said to her it was okay to give up.
Its been almost 6 months since mom has been gone, and EVERYDAY I still ask WHY?
I needed her still.
did god not see that?
I keep telling myself  he must have been to busy to see that, because now everyday I go though each day with a broken heart.
I miss her so much it hurts.
Will this guilt/pain just go away? I know its not my fault,
 its no ones fault,
but a part of me says it is.

The time I had with mom was so good, we only had disagreements a handful of times, she was my best friend and the one person who knew me the best.

No one will love me like she did.