I recently sprained my elbow falling from a height and sticking my arms out in front of me doing gymnastics. It started to swell on the day and the next day, but its slowly going down.

How long should I take off training for it till I recover?

Are there any strapping/taping methods I could use temporarily instead of buying an elbow guard?

Any suggestions it would be greatly appreciated.. past experiences?

Use the R.I.C.E method and see if it helps and maybe wrapping it will help with the injury.
But take enough time for it to heal completely because you don't want it to be injured again because it wasn't healed all the way.