I think the first thing you really need to do is to find something that you would want to eat in the morning - perhaps try going to the supermarket first thing in the morning and have a look around for something that doesn't turn your stomach. There are plenty of healthy things you might want to try eating for breakfast, maybe some cereal, or some fruit with natural yoghurt, perhaps even just a granola bar or some toast to begin with until you get used to eating in the morning? Since most breakfast meals seem to have a lot of dairy, maybe that's what is putting you off breakfast in the morning? You can still have a healthy breakfast without dairy though. Something I really love is a banana on wholegrain toast. It might sound a bit weird but it's absolutely delicious, you should give it a try! I know a lot of people who like to have banana and peanut butter on toast, maybe that would be more appealing to you?
Also, you don't have to have breakfast as soon as you get up. If I have time in the mornings then I often like to wait a while before I eat anything, to get used to the idea of being awake. I also like to do a little exercise before I eat - I think it gets my metabolism going. Maybe you could try that? Maybe after some exercise you'll be starving for something to eat? I like to skip in the morning, it's great fun and it really gets your heart racing.