How do you get a public defender in one state when you live in another? Is it better for me to just turn myself in?

If you check the court records, you might find you already have a public defender appointed.

I don't ever think it's a good idea to just turn yourself in. You should apply in Oregon for a public defender. It doesn't matter where you live it matters where the charge is from. When I was a public defender in Washington I had Canadian clients. Apply for a public defender. Next, call the court to see about a Warrant Quash. You may still have to post bail but at least you'll be able to explain why you've been gone for so long and tell the judge the steps you are taking to get the case resolved. Make some calls and talk to an Oregon attorney before heading to the jail.

Call the court and ask for the number for the local PD office. Then call and ask if they can help you.

Before you do anything, call a private criminal defense attorney in the jurisdiction where the case is filed and ask them all your questions.

I'm sorry you are having to deal with this situation. Before you make any decisions about how to proceed, contact the Oregon State Office of Public Defense (OPD) and explain your situation. OPD should be able to tell you which public defense group you should be contacting. The Oregon State Bar website has a section explaining how to get screened for a public defender. At the bottom of the website page, it lists the phone number for OPD. I have included a link to that page. Best wishes for a successful outcome.