How can one distinguish between an affliction that ought to be striven to remove and an affliction that ought to be endured to attain reward from Allah?

The issue of preferring patience in tribulation over abandoning treatment, versus seeking treatment, is relative. Treatment is better for the general populace, due to the saying of the Messenger of Allah, peace and blessings be upon him: "Seek treatment, for Allah has not sent down a disease except that He has sent down a cure for it." Patience is required from a believer in all circumstances, and seeking treatment while anticipating reward does not contradict patience. Abandoning treatment may worsen the illness.