will eating healthy and staying skinny really keep my boobs from growing/is it?

sometimes big boobs are gross. and sometimes smaller boobs are cute. trust me.

don't worry
You're thirteen, which means your boobs are still growing, and they'll keep growing for a while. (I'm 16 and I just recently went up a cup size)
As long as your chest is in proportion to the rest of your body, you'll look fine.
Also, if those other girls have more meat on their bones, they'll undoubtedly have bigger boobs - boobs are fat, so if you have more fat, you'll have larger boobs.
Keep eating healthy. Most of those girls probably wish they were skinny like you anyway

Use lotion and massage them they will get bigger since you are still growing