Making Nipples more flush to the chest. Sewing the Areola to the Chest wall.

[luxe89]

P

[Paa_Paw]

First you need to realize that the nipple is actually tissue that responds to heat and friction in the way you describe normally.  We used to call that a nipple hard on.    It happens to be 100% normal.
Next you need to realize that you are passing judgement far too soon.  The skin heals in a couple of weeks, but the underlying tissues heal more slowly. 
Third, the nipple needs to be free to move with and in relation to the Pectoral muscles.  If it is tied down, as you suggest, it would look most un-natural. 
I am not a Doctor, but I am a bit of an artist.  Would you be so bold as to try and tell a Michaelangelo how to sculpt a piece of Marble?  The PS is sculpting in tissues. Give the artist his liberty and he will do a much better job than if you supervise.  

[Dr. Elliot Jacobs]

Treatment of puffy nipples is achieved by adequately removing the breast tissue beneath the areolas -- NOT BY SEWING DOWN THE NIPPLES TO THE CHEST WALL.

Do yourself a favor and get another surgical opinion.

Dr Jacobs