I highly recommend you contact a lawyer, who can work with you to resolve the matter. If you have an outstanding warrant, you need to immediately take care of the situation, or things will only get worse. A lawyer can work with you to understand your situation and what your family can, and cannot, cope with. They can then work with the DA's office, and the courts, to negotiate a solution that gives you the most benefit. Feel free to call me if you'd like to discuss your options. Also, you can find other good attorneys through this site. Finally, you can contact the Oregon Bar at 503-620-0222 you can refer you to an attorney.
I agree with Mr. James answer above. TIme is of the essence and the quicker you can hire a lawyer the faster you will be able to formulate a strategy to minimize the consequences of this. Good luck.
You do need a lawyer before you turn yourself in if you want to minimize the chance of jail. Be aware that no attorney can guarantee you that you will avoid jail. You should also try to hire a lawyer who is familiar with the Court where your case will be heard.
Relax. You will be fine. The chances of you being arrested when you appear to clear the warrant for your arrest will be far less if you have a lawyer by your side when you see the judge. Having a lawyer tells the judge that you are serious and committed to seeing the matter through to completion and not running away again. Good Luck.