God I need some answers

Is it possible for one to believe in God and then question his existence when hard/difficult time comes and we want Him to show himself? I have been bombarded with images of destruction, pain, and mourning. The images on TV just make me want to speak to God and know why so many people are dying or have to die. I know God’s ways are not our ways and our ways not his. Thousands died in Burma and another in China. Let’s not even go to how many souls that dies on a daily basis in Africa. I love GOD, I seek to be close to him yet I am not too sure if he will be happy with my questioning why things are happening.