Can you put neosporin, pain relief cream, on a second degree burn?

Yes: That should be fine for smaller second degree burns.

Second Degree Burn: Neosporin is helpful for the treatment of second degree burns. It is essential to keep the wound moist until the skin grows back. At that point, the wound will no longer exist, it will not be painful, and treatment should then be changed to a water-based skin moisturizer.