Will my Nipple Grow Back Out?

If you had slough of the nipple, it will not regrow.   Your plastic surgeon can discuss options for you including nipple reconstruction via a skin graft or tattooing to create the appearance, but not the height of the nipple.

Sarah-- A photo would help answer this.

Whatever tissue was lost is gone and is not likely to regenerate. If the appearance is quite different from the other side there are ways to restore the appearance, but it would probably be best to wait for several more months, since the recent manipulation of your areola caused some tissue loss. Typically, pigmented skin from the areola is used, and that would be at risk for tissue loss if done too soon after the recent surgery. 

If your surgeon doesn't do much breast reconstruction, you might want to consult with one who does, because nipple reconstruction is quite common as part of post-mastectomy breast reconstruction.

Thanks for your question, best wishes.