Hi fondu my dd (now 11 yrs) went through a similar period of sensitivity last year and we also live abroad, she is also an only child, and she is also being educated in languages other than her own, so I just wanted to send my sympathies! I know how worrying and stressful the situation can be!
It's not always easy being the outsider, and having to express yourself in languages other than your own, even when you have a good grasp of them, can be challenging sometimes. Also, the education system here is quite formal and rigid and ; which I think can sometimes be difficult from someone with an English culture when our language can be so non-literal!
At the time, dd was in a group of three girls at school with whom she was having disputes and vice versa. She was also over-sensitive, over-fearful (of spiders and vomit) and couldn't seem to 'muck along' with the other children/take disappointments in her stride. She had days off school through anxiety and stress which added to the problem, because she got behind with school work and was even more out of sync with the other dc in her class.
Five or six months on and dd has overcome all the problems totally; and is much, much happier and confident within herself now. Tbh, I think it was just the natural process of growing up that helped the most, but it was suggested by the school that she see an educational/child psychologist for a few sessions and I think that must have helped too (although dd said what was discussed was a bit boring and obvious!). Maybe it was just the process of stepping back, getting extra attention, addressing her concerns that helped the most; rather than what the psychologist actually said or did ifyswim. In the end, they only had about seven sessions in total. The psychologist said that dd was very hard on herself and self critical and so I was able to take the cue from that and lighten up a bit about house rules etc etc and let her have more control over her own decisions. DD also gave up ballet temporarily (more stress/rigid rules) - in fact she gave up most extra-curricular stuff for an entire year - but she did also focus on an activity that she excels at (singing) to build up her confidence.
Having the school and teachers on board helped a lot because we were all working from the same hymn sheet as it were. The teachers talked to dd's friends and they all came to a resolution about how the friendships would work in future and they had to write one another letters, citing one anothers talents and individual positive characteristics and suggesting where they might have themselves have gone wrong etc etc.
I'm not sure a special diet will help but obviously eating healthily, with lots of veg and fruit and not too much junk food and sugar, and getting lots of sleep will help. DD has a children's meditation tape that helps her nod off.
The other thing that helped (that seemed counter intuitive) was being stricter when she was anxious about NOT having days off school; and that way she didn't miss work, didn't get behind, kept in sync with her classmates and built more resilience.
Sorry that was such a long post but I just wanted to let you know that "this too shall pass!". At the time I was terribly stressed about dd and questioning our decision to educate her abroad etc etc but as it happened, it was just a kink in the road! I have no doubts there will be others but just wanted you to know that you can get through it!
You might also get more suggestions if you re-post in 'living overseas' too!
Good luck to both of you!