With swelling like that it definitely sounds like you have a serious hair allergy. An antihistamine like Benadryl probably would be helpful. Hydrocortisone cream isn't a bad idea, either; if nothing else, it makes the itching more tolerable. Drinking a lot more liquids might help, too, by getting any irritants out of your system.
Sorry dude. I'm one of the lucky few in this world who is immune to T's hair. In fact, I'm also immune to poison ivy. Right now, the only thing that I am not immune to, as far as the causations for allergic reaction, is myself. Remember some of my posts back a while ago when I said I almost died from a severe allergic reaction? Well, they finally found out that it was nothing external. My body started producing chemicals that, for some strange reason, my body is allergic to. I am now on constant medication until my body stops making the chemical.
Hydrocortisone cream is probably best. Unfortunately, the non-prescription preparations tend to be on the weak side. If you can get a doctor to prescribe some stronger hydrocortisone cream, that is better. I have a real problem with poison oak (fortunately none yet with urticating hairs) and some prescription stuff I have works wonders.
If it gets real bad, go to your doctor and get a cortisone shot.