I've found that using supportive bracing, which also works as compression can help, e.g. aircast or similar products. Compression as suggested previously has seemed to work better for my patients than the icing/heat unless the patient has pitting swelling, Then icing has worked to reduce that and inprove circulation.
I'm less concerned about the swelling though, once it is getting less and occurs more after moving around, because that is expected (dependent swelling, reorganisaton and remodelling of tissue). I am concerned about reinjury of whatever structures have been injured, and so the P in PRICE system - Protection (splinting, casting, weight bearing status), and the C of compression, seems to be the most important at this point.
Strengthening is a really good idea, but with guidance at this point, to prevent further injury and protected, probably in water, varying resistance with speed and even temperature( so the two could be coupled).
Icing could then be used as suggested to control the swelling that may be caused by microdamage to scars as the tissue reorganises.
Have you been referred to /seen a Physiotherapist, Gemma?