My son has gone through a lot of what your DS has. We even went private too. He's now 17months and it's mostly gone (does flare up every now and then). He's only on Hydromol and the odd hydrocortisone 1% for flare ups. It's a long road, just wanted to hold hands and say it'll be easier as he gets older but hope it gets more manageable soon 
One thing that helps my DS whenever he does have a desperately itchy flare up (usually around his cheeks when teething or after eating, or arms/legs when tired), I usually always dampen a cotton cloth/muslin with cool (sometimes cold) water and pat down the hot/red/itchy areas. The cooling effect really does work for my son, have you tried it? Works for some, not for others, but just wanted to share. It's usually at night, we just lay there together and I cuddle him and pat his itchy spots. If the cloth gets too warm it doesn't work, so I usually have a little bucket nearby to rinse the cloth. I don't apply any cream if he is actively itching an area, I find it makes it worse for him.
There was a period, definitely waaay before he turned one, when I had to give him some piriton just for him to get to sleep 😔. My doctor reassured me it was okay, and at least he would have +4 hours reprieve. I only ever used it at night and only one dose. It helped him fall asleep, and if he did wake itchy (after the piriton had left his system), it was easier for him to fall asleep the second time.
My apologies if my post isn't relevant, I just wanted to share my experience. It's not nice watching them itch 