oh dear emma :( so sorry it's so bad.
first off, can you keep water / any sort of liquid down? This is really important. You can check if you are dehydrated if you get some Ketostix from any chemist or from Amazon. YOu pee on them and check the colour they go; if it's more than 3 you need to get medical advice. The headaches may be dehydration related so please, do check. How much liquid are you managing to keep down a day?
Secondly, there are quite a lot of meds you can try. Cyclizine is actually one of the mildest and it sounds like you need something stronger. Very few doctors are experienced or trained in hyperemesis, and they are usually not up to date with it. Sadly, he's right that there is no magic bullet and if it's this bad, you're unlikely to feel really ok. But there are drugs to help other than buccastem and cylizine and there are also some hints and tricks that help with getting liquid and food down you, even if they don't make you feel better.
Ok, the governmental body NICE which lays out guidelines for all doctors in managing illnesses says
"Goals: To reassure the woman that nausea and vomiting are normal in pregnancy, To reduce nausea and vomiting, To reduce time off work and other lifestyle disruptions caused by symptoms; To prevent complications" cks.nice.org.uk/nauseavomiting-in-pregnancy#!goals
The drugs they recommend are here: drugs commonly used for N+V in preg. Cyclizine is usually prescribed with B6 and it's actually the first line of defense.
These drugs are not just 'off the internet recommendations' they are the government's own institute's guidelines.
Can you go back to the doctor with a partner / friend who can advocate for you? it really does sound like you need something stronger and it's hard to put things clearly or keep persevering when you feel like shit.
If the doctor is not helpful there are a couple of other options. One of the helpful sites that lucinda metions in the original post has a helpline with a very experienced doctor who will ring you back.
lastly, there are a few things that can help with keeping liquid down. Lucinda's sites have some hints and finch has a great list of high-liquid water foods, if you have any time of day when you can eat something.
HG really can be hellish and make preg hell. We're always here for support and to listen. We've all been through it and know what it's like from the inside.