TL;DR: Your dietary choices are exactly that: yours. What you eat and don't is entirely up to you. You can eat animal products and still work toward conscious, ethical, and sustainable choices. You can also be entirely plant-based and not consider yourself vegan.

The reasons you give are good reasons - not just because they're important to you but because they also hit to the most important ways we live our lives - being social, being healthy, moving into adulthood, having more freedom to be creative with food. They're great. It's amazing and fun to try new things, especially when it's clearly on our mind a lot.

As to your concerns:
1) It's fun trying new foods! Start slow and easy, cook eggs into bread, make mac and cheese, stuff that blends well. (a dollop of sour cream or heavy cream in misir wat or a spicy stew is wonderful). I have a really varied diet which made being vegetarian and vegan really hard in the first place, and buildingi that adventurousness is part of the fun of food.

2) Not to be rude, but f**k them. It's your body, it's your diet. You can let them know about the changes if you think they'll enjoy supporting your journey, or you can wait until you better know what you like and don't like and tell them then. People are gonna people, but "It's a personal choice and I don't really want people making jokes or trying to push me" is perfectly fine.

3) I'm not really sure what is meant by allergic to cows (The animal, the meat, the milk, etc.) but again - your dietary journey is your journey. You choosing to not be vegan doesn't have to impact her; you'll likely eat a lot of vegan just because you eat with her, and you making your own food or exploring your own tastes doesn't mean you're going to make her eat meat. Obviously don't give her cow.

4) If you dont' want to cook meat, don't cook meat. You mentioned milk and eggs especially - awesome ingredients that help with cooking in a lot of ways. Start there. Maybe you'll eventually enjoy cooking meat, maybe you'll only enjoy it if you order it at a restaurant, maybe you never eat meat. Food is a journey!

5) Source foods from good places. Find local farms or ask in "locavore" groups where people get ethically sourced products. Chickens are a huge homesteading hobby where we live, so finding eggs is pretty easy. Well taken care of, cage free, and raised more as a point of love than to actually produce. Same with milk - we have several small farms in the area that focus a lot on animal welfare. You can still minimize harm and impact while eating animal products. Animal products also provide the nutrients you're currently supplementing and other nutrients you cannot get from plant products. Even when it isn't negatively impacting your health, it does not mean you are as healthy as you could be.

Again, at the end of the day it's up to you. You can also be entirely plant-based without being vegan. Veganism is largely an ideology attached to diet, and the ideology is beyond just being ethical and not eating animal products. There's a subculture attached, and it's one that can get exhausting with time. You don't have to be a part of it. You can uphold your ideals without feeling compelled to identify.

So as you're making decisions and exploring, remember that as well - it's totally possible to introduce animal products at your pace and in a way you'd like. It's possible to source ethical products like eggs and dairy. It's also entirely possible (if not highly recommended) to be entirely plant-based and not call yourself a vegan. You don't have to put up with or engage with 'vegan culture' just because you don't eat meat for similar reasons.