thin-skinned 
adjective
Sensitive to criticism or insults: he isn’t the only successful politician to be cliquey and thin-skinned...
- I am not very tough yet, I am not very hardened - at times this sensitivity may make me thin-skinned about criticism.
- Why are these defensive-sounding scientists and thin-skinned writers getting so overexcited?
- He is a clever bully, brutal in his criticism of others but so thin-skinned that he resorts instantly to the libel laws to cow his own critics.
Synonyms
sensitive, oversensitive, hypersensitive, supersensitive, easily offended, quick to take offence, easily hurt, easily upset, touchy, defensive;
paranoid, neurotic
rare umbrageous