How can the Hadith, "Indeed, Allah has pardoned for my Ummah what they whisper to themselves or what their souls harbor, as long as they do not act upon it or speak of it," be reconciled with a person's feeling of self-admiration or arrogance due to a good deed, even without uttering it? And does this necessitate seeking forgiveness?

The actions of the heart are, by consensus, subject to accountability. As for passing thoughts or what comes to mind without firm resolve, these are forgiven. Ibn Taymiyyah said that the pardon for passing thoughts applies to what is not a firm intention. However, a firm intention must be present if it is within one's capability; and if it is not possible, then some of its مقدمات (preparatory actions) must be performed. Actions of the heart, such as envy and conceit, are, by consensus, subject to accountability if they become settled and complete.