Yes, Faye, allergies are a nuisance. I always had itchy skin until I worked in Thailand and hand-washed my clothes in cold (well, it wasn't cold by British standards, but it was 'ambient') water with a very small amount of washing powder. I used to leave things to soak. When I came back to Britain and started using a washing-machine again, the itching reasserted itself. That's when I started to wonder.... So, from then (thirteen years ago) I investigated: discovered eco-balls, which I used for years (grey whites, tho no doubt 'technically' clean), then soap pods (soap nuts) which I still use. I also use Ecover laundry bleach for the occasional hot wash of things that need brightening up.
My whites stay white, I kill nasties if there are any lurking, and my skin is fine.
Are you able to get Essential Care Gentle Herb shampoo where you are? It does contain citric acid as a balancer but it has no perfume or other nasties.