lilsmum - sounds like you are having a tough time of it. Are you on your own? Is there anyone that can give you a hand - at least so you can get some sleep or just someone to talk to and for support?
Re the eczema - none of mine have had it so I don't know what to suggest. I know my friends ds and dd have it quite bad and she finds it eases off if she cuts right back on bathing them - she only baths them once a week and when she does, she baths them in just water and uses acqueous cream to wash and she smothers them in it afterwards. When dd is asleep could you put socks on her hands to stop her scratching?? During the day I guess you'd just have to try to keep her creamed up to ease the itching and keep her occupied so she is distracted.
Do you know why she might be waking at night? If she feels a bit under the weather, how about just bringing her in with you for comfort till she feels brighter? Do you need to cut back on her nap in the day?
About eating - well, I know how you feel as both ds1 and ds2 are terrible eaters. I'm afraid that is one frustration that you might have for a while. I think all you can do is keep up her milk intake, keep offering her small amounts of food. If she won't eat a meal, how about having a plate of little things just around in the lounge that she can pick at when she fancies something - breadsticks, grapes etc. If you are really worried about her food intake, could you give her some vitamin drops to supplement her?
If you are really unhappy and really struggling, go back to the HV and tell her so - tell her you really need help.
Sorry if I've not been much help - it's been a while since I had a 10 month old.
xx