Does tihs exist for the 15 day dl? I have an injury prone player who is injured  for 12  days, will putting him on the 15 day dl do anything (don't need the roster spot)? 

If he lost rating points due to the injury, he's not going to regain any of them unless he's put on the DL.

Does it work on a 15 day DL? or only the 60 day DL? 

How long will it take for him to regain points? He lost a point in contact, and a point in durability and health for a back spasms... 

The injury bug only affects the 60 day DL.

The lost point in contact could come back at any time during the season, either at the end of the injury, or throughout the season via normal development.  Assuming he's still young.  if he's an older player (say, in his 30's), it might be gone forever as part of normal decline.

The lost points in durability and health may come back at the end of the injury.  If they don't, then you won't likely see them until rollover into next season, with the same age caveat as noted above.