I have had psoriasis since I was 4 years old. It does get worse when my bg is high, but I have found that low carb certainly helps.
The psoriasis was at its worse when I was prescribed Atenolol for high blood pressure. There was no indication on the leaflet (some years ago now) that people with psoriasis should not take it as it could make it much worse, or could even cause people to develop psoriasis (there is now). I suffered for years with worsening psoriasis, constantly using steroid ointment to give some relief. However, I re-checked the leaflets on my medication last year and realised that I should never have been prescribed Atenolol in the first place. Once I realised this - none of my GP staff had made the connection -, some years after having been prescribed the drug, I insisted on being taken off it. One of the GPs at my practice told me off for reading the leaflets and was extremely patronising "you should not read the leaflets as you will just imagine that you have all the possible side effects, I know you". As a woman of mature years, I have become accustomed to being patronised, but this GP was another woman (whom I had met only 4 or 5 times) accusing me of being over anxious - I have never been like that.
Getting back to your query, I have recently read an article that indicates that diabetes is closely connected with psoriasis genetically - sorry I do not remember where I saw the article, it may have been on the psoriasis association website. My point is, check any other medication you are on for any linked side effects - not just the leaflets, but online where there is often more information. There is a website where you can enter your list of medications and it will tell you where there are any negative interactions - just google drug interactions.
I am on the low carb (keto) diet and my psoriasis is considerably better, although it is still there, this is the first winter for many years when it has been minimal and bearable.
Good luck.