Huge sympathies, it's bloody rubbish. Had it horribly from 6w-22w, hated every moment of it - to the point that DD is just about to turn 4 and I'm only just willing to consider doing it again!
Try and nibble little and often if you can, just a bite will help as low blood sugar exacerbates the nausea.
Go back to the GP and ask if you can maybe try something else. I started on cyclizine which didn't do too much, then changed to Stemetil which helped more. Next time I will ask to try others if I'm still being sick 6+ times a day, I think.
Re work - with hindsight, and considering doing it again, I would say stay signed off if you can't work. From now to 9-10 weeks you'll also have the 1st trimester exhaustion, which just makes it worse. This is such an important time to take care of yourself, and it's just a few weeks to be off. Once you start feeling less knackered you'll hopefully find the sickness itself a little more manageable.
Can you do any work from home or reduced hours? I'm planning on being brutally honest if I get it again and just telling them (politely, of course!) that they have a choice of me being signed off for a while, or still being able to work, just from home.
Hope you feel better. And yes, get thee to the hyperemesis thread!