Could there be osteomyelitis in arm after dog bite?

Can happen. Wound infections associated with animal bites usually have polymicrobial etiology,requiring broad-spectrum antimicrobials targeted at both aerobic and anaerobic gram-negative bacteria. Dog bite wounds can exhibit rapidly progressive soft-tissue inflammation.Deeper soft tissue can also be affected, manifesting as tenosynovitis, septic arthritis, and osteomyelitis.
YES. A deep and penetrating bite to bone could cause osteo.
Bad deep dog bite. The wound needs to breach the bone covering, the periosteum, to infect it. So it would very likely be a really bad, deep bite. Think something akin to an attack dog refusing to release an arm or leg.