You can definitely have eczema on your scalp but with Caucasians it's pretty rare because of the oils our scalp produces. The only real way to cure ezcema is to moisturize like crazy(shea butter/cocoa butter and the like) and NOT SCRATCH, period. The skin has abrasions that is letting in germs. That's what's itching. I learned this the hard way from having chronic eczema on my legs for over 25 years. All the Rx creams in the world didn't help. Raw shea butter gently rubbed on my skin after every shower is the only thing which keeps it at bay and my skin in tip top shape. At $7 a pound I couldn't be happier about my cure.
Anyway, about the itchy scalp. If you got some relief from the essential oils I'm going to throw one out here for you to try that I've had some bizarre luck with. I had a major case of the itchies a few months ago and had some sage EO laying around. Nothing else was working so I was willing to try it. So I put three drops in a 1 cup of warm water and after I was done shampooing I squirted it on my scalp. TINGLE ALERT!!! I could only keep it on for about four minutes before I HAD to rinse it off. My scalp was completely numb for about three days. NO itchies at all. Kept down the oil production, too.
Afterward, I researched sage as a hair herb and then it all made sense. It has long been used as a hair tonic to strengthen the scalp, ward off creepy crawlies, and even dye the hair(only if you do it a lot). I wasn't expecting the anti-itch and lessening of oil production effects, though. Very cool!
Each herb has it's own unique properties and value, that's all I can say. Nobody mentions sage here but I've found that even mundane herbs like sage can do some crazy good things for your skin.
I only had to use the sage EO rinse on my scalp twice and then never again. You might luck out the same way. My scalp healed over in a few days and maybe that's what stopped the itching, too. Itching is cyclical with damage to the skin.
If you'd like to try sage then I'd say it's definitely worth the splurge at your local nature store. Just don't use too much of it. I even use the stuff(10 drops per large load) in my husbands dirty clothes wash to get the funk out. Works like a charm. Lavender can't even hack it. I've tried.
Turn washer on let it fill 1/4 way, add your soap + 10 drops of spaced out sage EO. Let it fill up a bit more and then put the skankiest clothes down at the bottom of the wash with the cleaner ones toward the top. Even let it soak for an hour or so if you want. I don't. But you can. When the wash is over the clothes do smell like sage but the scent wears off in the dryer.
Sorry I went off on a tangent there but I've discovered some wonderful uses for EO's since I started locking my own hair. lol