First of all, have you tried non-thimble thimbles that stick on your finger, such as ThimblePads or UltraThimbles? I really like the small metal disc thimbles.
If you decide you STILL can't use a thimble, then you'll have to learn to not use your finger to push the needle through. Instead, grasp the needle between your thumb and forefinger and squeeze to push/pull the needle through the fabric. Hopefully this action won't make the muscles in your hands sore, or exacerbate any arthritis you may have. Personally I find it's easier to use the stick-on thimbles.