Yes. Inflammation is a good thing, but it must be monitored or it could over do it and cause more damage. The general advice is to start with cold just after the injury to reduce the initial inflammation, then relatively soon after switch to warm for a longer period, then alternate with short periods of cold with longer periods of warm.

Your pee is entirely blood byproducts (as the kidneys only filter your blood), your poop is mostly blood byproducts, as your digestive system is really good at absorbing almost everything that you eat. So there's also fibre in there along with anything that couldn't be broken down in time as it moved through (corn, nuts, etc…)