If they find something wrong, it's better to find out about it early when they can do something about it.

If they don't find anything wrong, you're perfectly normal like thousands of people who go for annual physicals every year and don't have anything wrong with them.

Don't know where you're at protocols vary from country to country, but you're coming up on the age where they may want to do a baseline mammogram, I think my Dr. told me she wants me to have one at 40 so that they'll have something for comparison in the future.
So that's something to think about. And really Dr.'s are used to nervous patients. They don't have to be scary.