"Self-conscious," "paranoid," or "insecure" could all work in this context, assuming that their friends' claims are not actually being negative.
Self-conscious - "Uncomfortably conscious of oneself as an object of the observation of others." [Merriam-Webster]
Paranoid - "Unreasonably or obsessively anxious, suspicious, or mistrustful." [Lexico]
Insecure - "(of a person) not confident or assured; uncertain and anxious." [Lexico]
Also, "irrationally anxious" could be used in this context.
If the friends were being negative, but the other person perceives those responses as the result of jealousy, then "narcissistic," egotistical, or "self-centered" (and potentially "vain" or "conceited") could be used.