3 weeks ago my husband started getting what look like bug bites on torso but now look like non symmetric squiggly lines and still itch. What is this?

Dermatographism? The squiggly lines may be from scratching when one has an oversensitive skin. Dry skin may be a cause for this and thus he should consider applying a moisturizer within 3 mins after bathing on a regular basis. Consider trying an antihistamine as well. If the problem persists, see a dermatologist.