You may not be requesting OT, but in some places, if you are there 10 or 15 minutes (or more/less, in some places) before or after your 12 hour time, it's automatic overtime on the clock. This is how it works where I am. This for me, means, if I don't clock out by 7:48 p.m., automatically, OT and they don't take kindly to paying out massive OT for any reason, unless it's staffing shortages that lead to it. Yes, it's only a "few minutes" here and there but it adds up if this is done often enough by too many staff members. I would be surprised if your manager did not get VERY excited about this (unless for some reason you are salaried, which most staff nurses are not).
Be careful about this-----if you are at all unsure, ask your manager or Human Resources how it works. If you keep amassing lots of extra time, they (mgt) will take notice and not be pleased.
I know you want to put the patients first. That is what makes you a great nurse, I am sure. But you have to be aware of all the issues that involve staying extra after your shift. If you are not clearing this with your charge nurse and/or manager, don't be surprised if they confront you sooner, or later.
Also, you have to know when it's time to draw a line between getting too personally-involved and being therapeutic in a professional way. This usually comes with experience. Also consider if you get overly-involved, you may be on a road to burnout which does neither you, your coworkers, or your patients any good.
The above suggestion about coming in the next day to check on the patient and listen to her story, is a great one. I do that often, also.
Good luck and keep on being so caring. We need nurses like YOU.