How can I continue to be active with a stress fracture without worsening the injury?

Heed MD precautions. Discuss strategies with your treating physician as he/she will know best. Limited or no load bearing is usually prescribed for a period of time to allow the injured bone to heal.
Myofascial release. You need to support the area locally - find a mld/cdt therapist who can help you with kinesio taping, myofascial release, or the release of the network of soft connective tissue in the body. With proper support to area you can continue to be active. Supplement with vitamin d3, glutamine and carnitine for nutrition to the injured areas.