Using heat early isn't going to cause any damage, but right now the goal is to actually RESTRICT blood flow to your ankle (without cutting it off). Restricting blood flow reduces swelling, and the ice also numbs the nerves so it hurts less.

Definitely keep the bandage on as much as you can handle (I personally can't leave mine on for more than 10-15 minutes at a time if I'm moving around because it starts to dig into my foot), and ice for no more than 10-15 minutes at a time.
Honestly, the only time where you should use heat is if it starts to bruise (alternating between constricting blood flow and enhancing it actually speeds up your body "flushing" away the dead blood cells causing the bruise).

Although it CAN help with pain at times, since heat is relaxing. I still personally wouldn't use it until after about a week since the injury.
At least you were able to get it care soon after the incident. It took me almost a week before I was able to get a brace, and I couldn't afford to take any of that time off from school. My ankle never healed properly because of that, and - although it's gotten better - I still have trouble even walking for very long.
