Sick baby emotions

This is the first time my baby has been sick with anything worse than a cold. He has the stomach flu, and has been vomiting every hour or two for the last 24 hours, and he has a fever.

I'm taking care of him and cuddling him and following the doctor's recommendations. But on the inside, I'm not handling it very well. Aside from the not sleeping, and the mountain of vomit covered laundry... it's just so hard to hear him cry. Because he's crying for milk and I'm refusing. All day he wants to nurse for comfort and I am supposed to limit how much he drinks at a time because too much makes him throw up. So I have to say no no no and then when I can finally say yes, I have to pull him off after just a few minutes, making him cry harder.

It doesn't make sense to him. He's asking for this simple comfort, and I'm refusing him. He looks so sad and confused. After a night of not sleeping and a day of his sweet sad cries, it doesn't make sense to me either. I know this is irrational but I just keep thinking why am I even alive if I wont even comfort my own sweet little child. It must feel to him like I'm betraying him when he needs me most.

I don't know what I'm even asking. Tips I suppose for how to comfort a sick child who doesn't understand why you won't do what they think they need. Advice on how to handle the heartache maybe. Reassurance of some kind. I just want him to feel better.