What would help my sprained ankle heal quicker?

To be honest, at this stage the injury will take about the same amount of time to heal whatever you do. I would recommend gentle exercise to reintroduce a range of movement to prevent stiffness. Continue to elevate the limb whilst resting to help with any remaining swelling.
Stop exercise if the pain worsens etc.

Some sprains can take as long as a fracture to feel fully comfortable so don't be surprised if you still have discomfort for several weeks yet.