Am I exceeding the maximum ratings?
Yes, you are exceeding the specs. Look at table 6.1 of the DATASHEET on page 3:



It clearly states the maximum difference between the V+ and V- pins is 16V. This means you can have +8V and -8V, as the difference is 16V.

As you have it right now, your difference is 30V, which is almost double the maximum ratings. Chances are, you have damaged the op-amp and it will need to be replaced. You should ALWAYS check the maximum ratings of any IC you are using if you are worried. If you can, try and be within the maximum, so +7.5V and -7.5V would work nicely here, for a total of 15V supply. 

Although directly under the Absolute Maximum Ratings, it does state: 


  Stresses beyond those listed under Absolute Maximum Ratings may cause
  permanent damage to the device. These are stress ratings only, which
  do not imply functional operation of the device at these or any other
  conditions beyond those indicated under Recommended Operating
  Conditions. Exposure to absolute-maximum-rated conditions for extended
  periods may affect device reliability.


Some people new to electronics could take the maximum to mean that is what is OK to use. The other bit that should be looked at is the Recommended Operating Conditions:


Making sure you stay above and below the min/max should make sure the device works as specified, however, the Absolute Maximum Ratings table should always be checked too.