I recently went thought this when my employer (I get reimbursed for a private policy) wanted me to shop for better rates. I can understand your concerns. I actually talked to my T about this quite a bit.

The best advice I have is do your research. There are companies or state policies that will cover you, but you might have to do some research to find the best policy for you.

The worst part of the application process for me was answering question after question about my mental health for a policy that didn't even cover mental health!

The other thing I am doing is getting my free yearly report from MIB. (It's like a credit bureau of health information that insurance companies use.) I think it only records info when you apply for private coverage, but I like to keep tabs on what information they have about me. Just like a credit bureau, they might have errors in their information. http://www.mib.com/html/request_your_record.html