People living with chronic health conditions often have to take care of multiple medical, logistical, and everyday tasks, including monitoring symptoms, following treatments, going for appointments, as well as managing work, familial, and social obligations. Unlike shorter illnesses, chronic health conditions are lifelong, often requiring constant monitoring and management, and as such, it is challenging for the individual to manage their daily life alongside their health, all by themselves. Further, people often experience stigma around their self-image and abilities due to their chronic conditions, further making acceptance of and life with the condition challenging. In this work, I look into how people living with chronic health conditions informally share the responsibility of managing their health and affected daily life activities with people in their close circle. I conducted in-depth interviews with 16 people living with chronic health conditions who collaboratively manage (or "co-manage") at least some aspects of their health with people in their close circles. I report on their (a) current co-management practices, including their use of technology to facilitate the same, and (b) experiences with stigma and its impacts on disclosure, support-seeking, and communication around their health, in different environments. I found that people appropriated different tools and technologies to monitor, coordinate, and collaborate with their co-managers. The nature of their relationship with co-managers and the physical or virtual space within which they co-managed were also key in shaping their current practices. I further identified avenues for designing technology to support people's diverse co-management needs, such as collaborative tracking, shared-space coordination, and navigating stigma during disclosure and support-seeking, contributing to HCI literature on designing for stigmatized health topics, chronic health management, and collaborative care.