I have dealt with similar things, and still do to a point to this day.
I used to say that my biggest fear was of being alone.
One of the things that helped me was to identify why. What does being alone signify to you? What is it about being alone that scares you?
For me it was many things, and more complex than just a "fear of lonliness", I was afraid of being unloved, of being rejected, of being unprotected. I felt frail and weak most of the time. And I had crazy thoughts a lot, a part of me just didn't want to be alone with my own thoughts, I wanted someone else there to drown it out. Does anything sound familiar?
I still have anxiety attacks every so often, always when i'm alone. I am a wife and mother now, but if I wake up in bed alone at night I am terrified.
The difference now is that I know the reasons behind it. I know that i'm not crazy, I know I will survive it, I know that I can be strong enough. When I feel a panic coming on, instead of letting it take over, I see it for what it is. I tell myself that i'm in control, that the threat is imagined, and nothing will happen to me. I literally have to talk myself out of it, but I usually calm down fairly fast now.
Another thing that I find helps, is the illusion of company I guess you could call it. Put on some background noise, music, tv, whatever. Look for something to do that will keep your mind (and preferrably hands) occupied. Read a book, bake some cookies, work on a hobby. Enjoy your own company.
I am concerned that you may be suffering severe depression/anxiety disorder or something of the like. You should go back to your doctor and work this through, not only for your own well-being, but for those around you. This behavior is counter-productive, and those people who you are clinging to so desparately will reach their limit eventually.
I know how you feel, i've been there. And you've come here for some help, which is a great start. Take it one step further and work it out with a professional, you have nothing to lose and everything to gain.
Take care.