Is poison ivy itching supposed to last weeks?

Up to a few weeks. It can last a few weeks. If more than this consider whether you've been exposed more than once, or if you still have intermittent exposure (ex oil from poison ivy on dog's fur can still get you). Wash all of your yardwork clothes, gloves, etc, if you have one shampoo the dog, wear long sleeves & pants when you're outside. If still a problem then see your doctor for eval of poss alt diagnosis.
It Could. Poison ivy reaction can last on average anywhere between 1-4 weeks depending on extent of rash and treatment. Also, scratching it can cause it to spread and increase the time it takes to heal. Oatmeal baths and cool compresses can help soothe your symptoms. Calamine lotion and benedryl may also be helpful. Good luck.
It can. Though it is usually due to people putting topical benadryl, (diphenhydramine) either creams or liquids, and developing an adverse reaction to it. If it has been going on for weeks, you need to be seen.