"We are not dizzy, but glad."
Translation:Mi nem szédülünk, hanem örülünk.
Just hanem boldog is wrong for two reasons:
You're contrasting two verbs here (even though you cannot translate them as verbs in English). Szédül means 'to feel dizzy', örül is 'to be happy'. Boldog on the other hand is an adjective, so you need to couple it with a verb saying 'we are' - vagyunk.
Boldog needs to be pluralised here because there are multiple people who are happy.
Mi nem szédülünk, hanem boldogok vagyunk.