While the facility may bend the rules, you as a nurse that worked so hard for her license should not. Giving meds without an order is considered 'practicing medicine without a license'. Not something that you would want to be charged with, ever.
If Tylenol was not working for her pain, you should have followed what your nursing practice tells you to (if you did, you did not mention it in your OP) and completed a full evaluation and followed this up with a call to the doctor. Often times, especially in women, a heart attack is presented with shoulder pain. While this may be an extreme example and the patient may have this history, it wasn't really mentioned in the OP. Also, when you 'bend the rules' and just try to throw medications at the problem, you could just be masking a symptom that could cause further injury...just something to consider.
Please, if this facility is what is causing you to be so casual with this type of nursing practice, find another one to work at. Even though you have graduated nursing school
and have obtained a license, your real training is now. Right now for you and will form the basis of your real 'working' nurses knowledge and I hope that you get the best training to give you a good solid nursing base. As another poster wrote, CYA but also, you really want to use the best nursing practices possible. Best of luck to you.