I have a similar job, which involves a lot of travel including long-haul. I didn't actually throw up more than a few times in my first trimester, but felt permanently really nauseous and exhausted, and it was pretty hard. The act of travelling definitely didn't help with the nausea, which seemed to increase with every day I travelled, but I had breaks in between and it definitely wasn't impossible.
I made sure I always had little snacks - and long-haul flights are quite good cos they give you loads of stuff like dry crackers and pretzels, which are just the ticket for nausea. I took Dr Karg's crackers everywhere with me, and had gum and sweets like Cherry Drops, Maoam or Starburst. Drank a lot of water, and cold cans of flavoured sparkling water like Ugly or Le Croix were an absolute godsend. Demand loads of ice in your drink everywhere you go. I had a big plastic travel cup thing that was permanently full of ice and I sipped on it constantly.
Rested wherever I could - felt bad about this as my job can be quite sociable and there are usually people who want to go for a meal or a drink - but I just made as much use of my hotel room as possible. Room service if you can! Often I couldn't have managed going down to the buffet for breakfast, it was better to get toast and cereal sent up to my room and work through it slowly and as I could manage.
Basically be as selfish as you can so that you can be on top form for the really important bits. You might well find that after 12-16 weeks you feel a million times better, I definitely have loads of energy now at 20 weeks and could definitely keep up with my duties for a good bit longer. If there is any way you can get your duties thinned out, do ask, but if you really have to be the one to do all this, you CAN get through it. Fingers crossed your sickness doesn't get too much worse. Good luck!