Stocking I'm so sorry to hear you are having such a difficult time but am glad to hear you have a good team there for you IRL 
Haquoi - I'm also a massive puker - I consider anything less than 10 vomits to be a good day
.
I have a stash of plain biscuits/crackers/bread-type things, fruit and some gummy sweeties. Either myself or DP box/bag them up into little snacks so when I feel hungry - or less sick - I eat them. I try to have a snack every 2-3 hours and a drink every 20-30 mins.
Personally, I find cold/frozen grapes, watermelon, very cold sliced Granny Smith apples and ice lollies relatively inoffensive but do find I go off things instantly. We have so much cereal I have wanted and then immediately can't face....oops 
If you are good with fluids have you tried more nutritious fluids? Milkshakes, full fat milk, soups, smoothies etc? Could be an easier way for you to get calories in.
The HG ladies are very wise and have some great advice too.