Hi, I'd like to help you with your question.
It sounds like your obsession could be one of two things- either you have feelings about this person because they fill an emotional void for you, or you have a type of Obsessive Compulsive disorder.
Since it sounds like you have been seen already either by your doctor and/or a therapist, then I am taking a guess here that someone has done an evaluation and has given you a diagnosis. Did the doctor or therapist indicate whether or not they felt you have obsessive traits? If not, you may want to talk with them again. Obsessive compulsive behavior is related to anxiety, so it may be very possible that is what you are dealing with. In that case, the medications will help, but therapy is also indicated. The medication can treat the symptoms, but to solve the problem talking to a therapist would best help you resolve the issue.
If you do not already have a therapist, talk with your doctor for a referral. Or if you attend church, your pastor might be able to help. You can also search on line at http://therapists.psychologytoday.com/rms/.
If you feel that your thoughts about this person is because of an emotional void, then you can work on finding new ways to fill it. First, determine what the void could be. Where you abused as a child? Was there a traumatic event in your life? Whatever you feel it could have been, look at exploring how it affected you and how you feel it has caused your feelings now. Also, you can explore these feelings with a therapist to get insight into how you can best address this.
Some of the steps you can take to help yourself right now include:
Letting yourself obsess. If you try to stop the thoughts, it only makes it worse. Think about it, but don't act on it.
Write out how you feel. It helps you clarify your feelings and also allows you to keep track of how often you feel this way, and your progress on recovery.
Educate yourself. Learn all you can about obsessions. Read books, search on line and learn what you can.
Do good things for yourself. Spend time with supportive friends and family. Take an exercise class, start a hobby, anything to keep yourself busy. You shouldn't ignore your thoughts, but if you focus on other things as well, the thought won't be as intrusive.
Here are some book recommendations to help you as well:
Overcoming Obsessive Thoughts: How to Gain Control of Your OCD by Christine, Ph.D. Purdon and David A. Clark
Coping with Anxiety: 10 Simple Ways to Relieve Anxiety, Fear & Worry by Edmund J. Bourne and Lorna Garano
Stop Obsessing!: How to Overcome Your Obsessions and Compulsions (Revised Edition) by Edna B. Foa and Reid Wilson
You can find these books on Amazon.com or your local library may have them.
I hope this has helped you,