The Old and New Testament teachings on the use of force seem quite at odds. Is the use of force ever morally right? How does the Lord want these things handled? In prison, this issue is especially hard [for me].
Actually, the teachings about use of force between the Old and New Testaments are not really at odds but, instead, complimentary, simply having different focuses on when, where and how. For example, both the Old and New Covenants teach that it is proper to use force in order to restrain evil and wickedness in the world, as well as for the defense of a nation. However, the one area in which force is not permitted is for the defense of the faith. As far as our faith is concerned, we must turn the other cheek and be willing to become martyrs. In regard to protecting ourselves from crime and our nation from foreign aggression, force is allowed by both the Old and New Testaments. The Bible does not teach passivism; pacifists usually misuse verses that apply to the defending of the faith and ignore the context, which has nothing to do with defenses against evildoers and national aggression.
To answer your specific question concerning your personal status in prison, the question must be asked: what is the motivation of the attacker? Is he attacking you because of your faith in Yeshua? If so, then you cannot use force to defend yourself. However, if he is merely attacking you because he is an evildoer, then you have the right to use all means at your disposal to defend yourself against him.