If I were you,I would tell Mei that there are a lot of obstacles in one's whole life while her shyness is just one of them,which is on her own decision whether to overcome it or escape from it.And I would also tell her that as her best friend,I have faith in her that she will accomplish great success in the contest due to her competence in English and I hope that she can have a try.
Meanwhile,I would tell the rest of the students that Mei is only a teenager herself,who isn't as confident as most of them assumed and will also be afraid of speaking in front of the public.Their confidence in Mei might become her pressure,which might even influence her performance.Therefore,they should give her more space and let her make her own decision whether to take part in the contest.