If I’m lactose intolerant and I breast feed my baby will I feel like I need to **** and throw up?

Your breast milk will only contain lactose if you ingest it yourself, so if you're on a lactose free diet your milk will not contain any lactose. Lactose intolerance and a dairy allergy are very different things but you won't have an adverse reaction to your only bodily fluid.

You're not going to be allergic to your own milk. Which you also won't be drinking...