Can nerve pain med help post op pain for digit widget when there's ulnar nerve damage, claw hand, crps?

Yes: All neuropathic pain will respond.

It can: Neuropathic pain is notoriously difficult to treat. Treatment involves many different aspects such as medications, nerve block injections, therapy, even surgery. While medication can have a good effect, it is typically not used alone. Crps itself usually requires a significant and multi-disciplinary treatment plan, and it is best treated aggressively and quickly/early!