Would my act be considered showing off if I asked my father to dig a well for my deceased grandmother at my expense, based on a dream that was interpreted as her needing charity?

It is not a form of showing off (riya') to seek your father's help to speak with a non-mahram man on your behalf, as long as you spend the money seeking the countenance of Allah. Riya' is when a servant performs an act of obedience or refrains from a sin while observing someone other than Allah, or when they disclose it, or love for it to be known for a worldly purpose, or it is seeking status in people's hearts by displaying acts of worship.