Sunburn, Hives, PMLE. If you mean sunburn, the damage is done and Hydrocortisone won't help much. Anti-inflammatories (ibuprofen), cool compresses, and skin hydration with soothing gels or creams can help with symptoms. Stay out of the sun completely and wear sunscreen/sun protection going forward. If you mean hives or a rash called polymorphic light eruption (pmle), talk to your doctor--cortisones can help these.
I would think not. This depends on what you mean by sun poisoning. If you mean sunburn, you're better off with sunblock/suntan lotion, which is designed to block ultraviolet light. Hydrocortisone is designed to lessen the body's reaction to the poison ivy and lighten the rash, so these are two different things. Therefore, do not use Hydrocortisone for sunburn.