For milk, there is almond milk, rice milk, and coconut milk, and soy milk, amongst others. Try more than 1 until you find your favourite. Consider one with calcium (check the packets), as calcium can be low on a vegan diet. If you don't know where to find them let us know what country you are in and maybe someone living in that country can help you. I personally find the quality on a par with animal milk, however sometimes I've paid double the price or something like that so keep that in mind. I actually eat cereal without milk. Have you tried that? Or just use the milk more sparingly if it does work out more expensive. Overall, I think you'll find that milk is less of an issue than you think!
Vegan cheeses are not as good in taste. Violife is the best one I've tried so far. You can get that in a number of countries now. Still, it's a taste similar or worse to the best animal cheese at a much higher price. Still, better than the intense cruelty of the daily industry. I am talking about cheese in general here. I don't know about a replacement for your specific type of cheese though.
I suggest you make double portions of stuff for dinner and then make a packed lunch for the next day to minimize on buying when you are out, and having to put up with junk food or limited vegan options. Even if you only bother to do this 1-2 times per week it will still be helpful and make a nice changeup.
I made this list of vegan meals I eat a while back. Keep in mind this is for super simple stuff. If you have time to do proper recipes you can do even better.
Mushroom + tomato + toast/bread
Pasta + veg + peppers
Rice + veg
Soy/lentil Burger + chips
Black bean burrito/tacos (I like sweetcorn in mind, or rice, or lettuce, avocado, tomata etc) + salad
Jacket potato + whatever you like
Sandwiches: vegan cheese with either tomato, onion or lettuce