How to cope with illness in my child so he doesn't know I worry?

Feelings are normal. Depends on the age of the child. A child also learns how to deal with the challenges from the parents. It's ok to let your child know that you're worried about him/her. It's not the worry proper, but how you cope with the worry. You might be worried, but still functioning. Finding support groups in your area and individual counseling to help you guide through your situation.
LOVE. Show the love and concern you always have to your child when he is sick and by hiding your worry with constant prayers.