How can I improve my mobility if I have significant arthritis in one hip?

Yes. Unilateral hip arthritis and consequential dysmobility, depending on its causes and stage of development, can be improved by treatment with anti-inflammatory medications and joint replacement.
Options. Physical therapy for stretching and strengthening of your abductor muscles, hip flexors, and it band can help. Nsaids/tylenol are good adjuncts. Injections of steroid or a lubricant (synvisc (hylan g-f 20) for example) can help in mild to moderate cases. Total hip replacement can be the definitive treatment. Discuss with your ortho hip specialist.