If you're throwing up every day, your teeth will be VERY weak. The acid from your stomach is strong. I know you're not thinking about babies, yet,but you will one day and this could compromise your future chance of getting pregnant. If you're on the road to recovery, keep going. Once you relax around food, it won't be an issue and your weight will remain stable.
You can drink black espresso, caffeine is a diuretic, so it will clean out your lower intestine, leaving a little extra room for your stomach (but if you do that, drink plenty of water. Throwing up leaves you dehydrated).
go swimming :) always makes me hungryyyy, or force feed if you have to.