I've been suffering with HG too, although not as bad as you from the sound of it. I also work full time, and had time off for it as I felt so awful.
I found it very exhausting and felt stressed that I wasn't able to do my job properly as I felt so sick all the time/was actually throwing up, so I can appreciate that it's a worry to take time off work but also know that you're not doing the best job you can at work anyway!
It's worth keeping in mind that exertion and stress can make it worse, so you might be better off resting up at home for a week or two to help minimise symptoms. As my GP said to me, your work will have to cover you and you just need to worry about yourself and the baby right now.
If the cyclizine is not helping, go and see your GP for a different anti-sickness tablet. There's several different ones that they can prescribe which are safe, and another type might work better for you.
Fingers crossed that it starts to pass as you get into the second trimester. I'm now 19 weeks and although I'm still taking the anti-sickness tablets I have left, I am now feeling much better than I was, with minimal nausea/retching and no vomiting for a couple of weeks.
Try and take it as easy as you can, and get plenty of rest when you're able. Good luck!