Hello. I'd like to help you with your problem.
It sounds like your co worker is giving you a hard time and saying things about you to your boss. You also said that you were accused of not properly notifying a client regarding services. I am not sure if the two are related, so I will address each one as a separate issue.
Regarding your co worker, I would continue to remain quiet on the issue. If your work is good, your boss is happy with your work and you continue to do your job well, what this co worker is saying will have little consequence. However, if your boss is having issues with your work related to what this co worker is saying, it is time to meet with your boss to straighten the situation out.
Set up a meeting with your boss to talk about your work performance. Do not set the meeting up based on the co worker and her talking about you. You do not want to appear to be affected by this co worker. Talk with your boss, focusing totally on your work performance. Ask how you are doing, ways you can improve and what you are doing well in your job. Only mention the co worker if your boss brings the situation up. And then only respond by focusing on your work performance. Do not personally attack the worker. You do not want to appear to be at his/her level.
If the accusation of forgetting to notify a family member of a meeting is true, acknowledge the mistake and say you will improve your performance next time. If it is not true, then say that but also say there is a misunderstanding and that next time, you will be sure the family member is notified.
It would not hurt to start keeping track by keeping notes on when you notify clients of meetings, noting the time and date and who you spoke with. If you can, do this with other parts of your work. As long as it isn't confidential information, it can't hurt to keep a log of what you do to back yourself up in case this happens again.
You mentioned your sister thinks you need psychological help. Do you agree with this? If you feel talking with someone would benefit you, it never hurts to try it. However, do not go to counseling just because someone tells you to. You have to feel that you would benefit from counseling.
There is also a good book that will help you with your situations. It is called The Power of Positive Confrontation: The Skills You Need to Know to Handle Conflicts at Work, at Home and in Life by Barbara Pachter and Susan Magee. You can find it on Amazon.com or your local library might be able to get you a copy.
I hope this has helped you,