Yup! I was horribly sick until 18 weeks or so with DS#1. (Lost 15+ pounds, and was eventually put on Zofran so I could eat.) With DS#2, I threw up MAYBE fifteen times the entire pregnancy, and all nausea was gone by 14ish weeks. Both are healthy, happy little boys. : )
Try not to worry--every pregnancy really is different. I'm sure your little one is perfect. : )