An open wound on my for arm, its pretty deep and it was self inflicted, it needs stitches but I don't want to go to the hospital. What should I?

See a doctor . The wound sounds deep so the potential for infection and further problems down the road is high- therefore you need to see a physician. Without seeing a physician- you will not know if it requires stitches, antibiotics, or even of there is tendon or nerve injury.
Go. Get help both for the arm wound but more importantly to get help on why you would hurt yourself...See talk to your family and/or get immediate medical help.