Sorry about your news, I recently found myself DQ'd as well (doc said bad knee despite my being able to outrun all of the other poolees).
From what I understand... once you've been DQ'd, you're DQ'd. You can try writing your congressman but I've read that's a waste of time.
I did some googling and it would seem that psoriasis is not waiverable and is an automatic DQ because you won't be able to be vaccinated for deployment.
It sucks but it's best to just accept it and move on.
Do not, under any circumstance, go to another recruiter and "forget" details of your medical history at MEPS because if the symptoms are ever to reappear and they do dump your history, you're in a mess of trouble. Many military people I spoke to about my issue said to just "forget" but, honestly, I wouldn't want to risk a discharge because I committed fraud.
Best of luck.