Oh you poor sweet baby!
YUCK!
I know the feeling...I vomit so hard when I am pregnant that it comes out both ends (literally). I have to strip my bottoms off when I run to the bathroom because the force of my vomiting makes me pee all over myself. This goes on for like 8 weeks...
I am not a doctor but as far as I know "NO" this will not hurt your baby. It hurts your abdominal muscles but the baby is nestled much lower than that in your warm little uterus.
You were right to take it easy though...don't go through all that and then still try and be "super mom" to your little guy.
This to shall pass, I promise!
Eat small, light and bland...for some reason oranges always helped me more than crackers and Sprite...but you never forget the first time you vomit up acidic oranges let me tell you.
Good luck baby! Hang in there!