Andrea, this is a difficult situation. I would prefer to examine you before giving you absolute advice, so please take what I am offering as suggestions for consideration rather than strict advice or direction, OK?
It does take time for dense connective tissues to heal. Your doctors advice to take time off is valid, though disappointing from a participation perspective. That said, dense connective tissues also need stress to help them heal so that they can actually tolerate stress going forward. I disagree with the advice you have been given on this basis: Graded exercise that is pain free and does not leave you hurting later is beneficial rather than harmful. Ice helps inflammation and edema, especially in the leg. Are you taking NSAIDís per MD instructions?
Are you wearing heel lifts in your shoes to unload the tissue?
My advice, seek another opinion from a doctor who runs...actually runs...call around and talk to the physical therapists and ask who is the best doctor for runners in the community. The PTís usually have a pretty good idea who they would refer active patients to.