There are things you can do immediately after known exposure or when the very first signs of itching appear. You are past that point. See a doctor. Get a steroid shot. One steroid shot isn't going to cause any health problems.
In the future, you can prevent poison ivy rash by acting to wash the invisible oil off your skin. Regular soap will NOT do it. Dawn dish detergent WITHOUT moisturizers will work, but the best soap is Fels Naptha. It's an old timer laundry soap in a bar. You can buy it at Walmart and some supermarkets in the laundry soap shelves. It'll cost about $2 for a bar. One bar will last all summer even if you use it on your legs and arms every day.
Wet the area with cool water. Rub the soap into a lather over the affected area. Rinse with cold water while continuing to rub the area back and forth with your fingers. It might take 2-3 applications, but eventually you'll be rinsing the soap off and your fingers will just... stop moving! You'll have rubbed all the oil off your fingers and the affected area. At that point, you hopefully have removed all your natural skin oil and the offended poison ivy oil.
If it still burns after this, do it again. It might take 2-3 applications.
Now, if you've put hot water on it or if you've sweated since exposure, your pores have opened up and the oil can get under your skin. At that point, you probably need to use Zanfel.
Zanfel comes in a tiny toothpaste tube and has a grainy consistency. You apply it following the directions VERY CLOSELY and it will stop the itching and remove the oil.
The reason I didn't mention Zanfel first is that it's expensive AND you must follow the instructions closely or it won't work. I hate to say this, but some people are genetically wired to ignore instructions. If... if... you can follow the instructions, Zanfel will work. Now, since the OP has a rash around his eyes, he shouldn't try either of these options. He should get to an urgent care center and get a steroid shot.
Even though Zanfel is pricey, it's cheaper than a visit to an Urgent Care center. I keep a tube handy just in case the Fels Naptha doesn't work. I run trails and get poison ivy 2-3 times a month. I keep a bar of Fels Naptha in the shower and use it on my legs after a trail run.