Is it normal to be scared of flying before becoming a pilot?
I think its extremely normal. The fear of the unknown is very powerful. When you are in control, you generally know what is coming and aren't surprised. 

Most pilots I know have no desire to sky dive. They love the freedom of flying, but falling uncontrolled is not enjoyable to them. 

When I'm not PIC, sudden drops give me that put in the stomach feeling. When I'm in control, that NEVER happens.