How do I apply for a visa when I have been denied entry to a country?

I am a U.S. citizen, who had been living in Sweden- with a permanent residence permit for the past seven years- and was attempting to visit my best friend in Scotland when I was detained, psychologically abused, and eventually denied entry on the grounds of being 'a threat to the nation'. I am on disability, have a regular 'income' from that. I have a place to stay in Scotland- four different people have offered me beds/spare rooms. I never requested asylum or permanent entry. In Sweden, even though I am on disability in the U.S. and qualified on multiple grounds for disability assistance in Sweden, I never requested or applied for any aid or assistance. My 'sponsor' in Scotland has disability assistance and her rent and utilities are paid for outside of her income. I have no idea how to proceed. Any help/advice?