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.
Figure 1. Vmax.
This line of the datasheet is stating that the maximum voltage difference between V+ and V- is 16 V.
You have probably damaged the op-amp.
I read your question as "yes I've read the datasheet, but its unclear". So let's address how to read the supply voltage range specification as the manufacturer Texas Instruments write it in their original product data sheet:
Supply Voltage (V+ - V-)... MAX 16V
You have a V+ of 15V and a V- of -15V. Now we use the formula from the data sheet and get:
(15 - (-15)) = 15 + 15 = 30V
That's the way to interpret this voltage range specification. So yes, you are exceeding specified maximum supply voltage range by 14V.