This may not help to hear right now, but your DCs love you, and you are certainly not fat and ugly, that's the illness speaking. No matter what happens, in the long run your DCs will want you to be happy and healthy. This is not the only holiday in their lives, they can have many more holidays 'of a lifetime', but only one you.
Making a plan for the worst case scenario is sensible and may also make you feel more relaxed, knowing that your safety net is prepared.
First things first - are you travelling with a partner or another adult who you can speak with first? They really need to know what's going on to support you and also in case things don't go well. If no-one is with you, can you call or message someone at home? You should focus on calming as much as possible and being with your DCs, let someone else do the running around. Make sure you are getting plenty of sleep, jet lag and other disturbances will only make you feel worse.
Next, can you call your doctor at home or a support team? They may well have medication or other suggestions to help.
While you're doing this, I'd suggest that your DP/family member / friend call your insurer to confirm what cover is available for preexisting MH issues. The insurer will usually have advice and suggestions for what to do in an emergency. If preexisting MH conditions are not covered (sadly, often the case), your support person should investigate the costs of flights home, this may turn out to be cheaper than care, as the US can be bankrupting.
If all else fails, take a taxi to the local
a&E - they have to treat you, regardless of insurance or nationality.
for you, you're clearly coping so well and doing amazingly to have got your DCs so far already.