Does cortisone in high doses damage the adrenal cortex?

Prolonged use, yes. Using steroid for a brief period of time of less than a few weeks probably won't have long term effect, but prolonged use will suppress it--it loses the ability to produce the steroid. Thus folks who need to use steroid for an extended of time often need to remain on it. The length of time varies, but using more than 3 wks typically would need a slow wean. Consult doc. Good luck.