No, personal data in GDPR is much wider than American PII definition.
Personal Health Information is only applicable in a specific setting (a covered entity). You telling your boss/friend/form about your health information does not make it PHI. You willingly disclosed that information.m, it loses its protected status.
‘Personal data’ means any information relating to an identified or identifiable natural person (‘data subject’).
Note the weight of the word “any” here.