I have suffered with Psoriasis for 15 years, scalp and body. I have tried pretty much every form of shampoo that is recommended with horrible results, but I have been using Aussie shampoo for the last 3 or 4 years and it is 100% the best shampoo I have tried. I find shampoos targeted specifically for people with scalp issues only seem to iritate Psoriasis, as it softens the skin and agrevates it more.
Also, yes sunbeds are recommended by doctors but they are specific sunbeds that contain UVB. Highstreet sunbeds only UVA, which isnt a treatment for Psoriasis. It does help to disguise it a bit, but it does not actually cure or reduce it and ultimately UVA is still damanaging to the skin, so not worth the increased risk of skin cancer IMO.
Google UVB combs. They can be pricey and obviously speak to your doctor about it first, but I know a few people who have said this really helped them. I have never tried it myself so can't really help, but there is a lot of information on the internet.
Also, after a few weeks of the treatment the doctor has recommended, if you aren't happy then go back and ask him to prescribe you something else. There are lots of treatments available and unfortunately not everyone responds the same with. With Psoriasis it is trial and error until you find one that works for you.
It is nothing to be ashamed of and I agree with the person above who said to build a relationship with a Hairdresser. If your uncomfortable in a salon at the moment, perhaps have someone come to your home? It's a lot more discreet and there are some amazing mobile Hairdressers out there. Another little tip, I keep my hair light to disguise any flakes. Stay away from all over tints as these can be really painful, but highlights are fine.
I hope that helps. Feel free to message me if you have any more questions xx