I really feel for you but I think you might need to play a longer game here and treat your deficiencies first.
Many of the symptoms you describe can be attributed to the deficiencies- I've experienced a number of them myself!
Low vit d for example can trigger a heightened immune response so could well explain your allergic reactivity to things such as light rash, joint pain and stiffness and slow skin healing
Low iron is also a common cause of a variety of symptoms that can make life miserable.
Have you seen an optician? If not then this needs to be your first port of call for the eye issues and also headaches, which could be eye strain. Blurred vision also points to an eyesight issue.
An optician will also be able to check for signs of any common eye conditions that cause itchiness and dryness, such as blepharitis, which is treatable.
If you'd like to start a family then I would also pursue this with your gp as a separate issue as the tests run into infertility and difficulty in conceiving, etc, may also indicate if there's an underlying issue you haven't identified yet.
I really do sympathise because I have suffered with many of the symptoms you describe and altogether they really do impact quality of life, however they may well have an innocuous explanation thats easily remedied.
Work with your gp to treat the deficiencies and other flags from your blood tests and see how you get on.
If the problem still continues when they've exhausted more typical avenues, they may well be more inclined to review the situation.
At the end of the day, as well, its much better to not have an autoimmune disease so if there's a more innocent cause for the way you feel then that's a win :)
You are, of course, entitled to ask for second opinions but I wouldn't be surprised if new doctors wish to rule out other more likely conditions first - its part of the diagnostic procedure.