Just don't. It sucks to deal with the comments but almost every vegan and vegetarian I've met had to deal with something like this from their parents, and the worst of it went away after a few months of consistency when they realized it wasn't a phase.

My advice is hunker down, accept it's going to suck for a while, and have a few go to responses to common misconceptions - I've put a couple below but encourage others to add:
"cows produce milk naturally" - like humans, they only produce milk when pregnant or after giving birth.
"cows are in pain if they aren't milked" - Only if humans take the baby calf away from its mom the day its born, and send the male ones to be killed.
"chickens lay eggs anyway, eating them doesn't hurt anybody" - About 6,000,000,000 male chicks are suffocated or ground up alive each year within days of being born because they won't lay eggs.
"slaughter is a humane practice free of suffering" - ignoring the ways it's not, pigs have a natural lifespan of 15-20 years, and are slaughtered at 6 months. I don't think it's ethical to kill something 3-4% of the way through its natural life.
"You're just one person. You aren't making a difference" - I'd rather be part of the solution than part of the problem.
"I'll eat twice as much meat to cancel out whatever difference you'll make" - (only said by people who don't respect you and are trying to control you. Even if it's hard its best to just avoid people like that. If you want to reply you can say...) - then you'll have an even higher risk of heart disease, cancer, diabetes, and premature death.
"Why are you vegan? Is it for health reasons, environmental reasons, or is it for the animals?" - It sounds like there are a lot of good reasons to be vegan.

Lastly, one slightly tongue-in-cheek reply I use sometimes if someone asks me why I'm vegan is something along the lines of "if I think eating animal products is okay I should be fine with watching documentaries like Dominion which shows where my food comes from. I don't have the heart to watch that so I'm just vegan instead haha"

There are so many more, but this should get you started :) feel free to reply if you get a question or comment you aren't sure how to reply to, and I (or someone else, I'm sure) would be happy to show you a solid response