I became vegetarian 2 years ago and I am slowly transitioning to be fully vegan, and yeah it's hard at first. I really missed chicken and cheese at first, but eventually you stop missing it and have no desire to eat it anymore and it's totally worth it. I feel way better now.
I recommend starting slow, just choose the meat and dairy free option whenever you can, gradually make healthier vegetarian/vegan choices and work up to implementing it fully into your diet. Some easy substitutions include using almond/soy/any other non dairy milk instead of cow milk in cereal and recipes, or having tofu in your dishes instead of chicken or beef (I know you said you didn't really like tofu, but tofu can be super great if you cook it up right. Look up some recipes.)
Also, make sure you are getting all the nutrients you need if you do cut out meat and dairy. Eat lots of healthy fats and proteins like nuts, beans, avocado, etc. Eat lots of vegetables, especially leafy greens like kale etc. Leafy greens have iron and are really vital to include in your diet. Also consider taking vitamins to help fill in any gaps.