Most people don't know that you CAN get adequate protein not eating meat--it's just a belief people have that you HAVE to eat meat to get enough protein. However, there are plenty of non-animal protein sources--as you mentioned, you eat eggs (animal byproduct, not animal flesh), and that's a great source of protein. There are a lot of grains, like quinoa that are an excellent source of protein.
Rice and beans are a complete protein (and beans have TONS of health benefits).
Some people say they felt poorly on a vegetarian diet, so I suppose everyone is different, and I'm not about to judge. I've been 90% lacto-pesco-vegetarian for years. I feel great at 60--no meds, I keep up with all my young friends in my yoga classes. There are LOTS of very long-lived vegetarians out there.
If you are feeling fine, and your blood & vitamin levels are fine, why worry about it?? The next time someone asks, how do you get your protein tell them, from grains like quinoa, brown rice and oats; plants like avocado, beets and peas; legumes like beans and chickpeas; nuts and seeds; and eggs.
Then show them this slide show about vegan super athletes:
http://www.treehugger.com/slideshows...dont-eat-meat/