Interesting! Sounds like a cool project! I do a fair bit of network analysis in my work, and just recently started tracking my own physio data - it would be cool to think about using a network approach to understand it.
What are you thinking for the network modeling? I could imagine a lot of different possible ways to model it (what would be the nodes and edges; having different time points as different network layers for a multi-layer temporal network; calculating measures of network structure (or node-level measures that represent body systems) at different time points to compare; modeling how changes to one node cascade to changes in others with a transmission model, etc).