My husband's right big toe hurts on the outside of the toe, no ingrown toenails or fractures. It's just the big toe not the joints. What could it be?

Several possibilites. Broken toe bone, dislocated toe bone/joint, gout, bruising are all possible. With his young age, watch closely and if not getting better in a few days, then get evaluated at a local minor er with x-ray. Go sooner if fever, worsening pain, redness develop. Be well.
Possibly irritation. From a shoe that caused friction and pressure to the skin.