Asylum in Chile

Hi,
I know this sounds unfamiliar for most people, but I'm a refugee from Syria, I have been in the UK for more than 16 years, and still struggling to be integrated, I speak English fluently, I studied in the UK, and worked so hard, but the UK is becoming an unwelcoming place by the day, and however hard I tried there are always obstacles in my face, and I know many people with similar situation.
So I'm really thinking about moving to South America, like Chile or Urugyay, the problem is I don't have a passport yet, yes you read it correctly after 16 years I have no passport, and the UK HO is refusing to grant me one. All what I can obtain is a travel document.
Also, I have a long term illness, so I'm worried about disruption in my treatment.
So I need to know, is it possible to claim asylum in Chile on the grounds of mistreatment by the UK as a host country, or lack of prospect of integration?
Please advise me, any information will be received with gratitude, as my situation is really bad.
Thanks