Can I play a spell after combat damage is assigned?

No, you cannot play a spell after combat damage has been assigned.

According to RiftJudge FAQ #3998 and FAQ #5308, the window for playing spells (both [Action] and [Reaction]) closes once you reach the point of assigning combat damage. The combat sequence proceeds directly to damage assignment and resolution, followed by the combat cleanup/healing step. There is no window to cast spells or play reactions between these events.